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Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary.

In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary.

A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display, as shown below. How far from the base of the pole should the end of the string of lights be anchored?

A right triangle with one leg marked 12 and hypotenuse marked 13.

5 feet

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Pam wants to put a banner across her garage door, as shown below, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. How long should the banner be to fit the garage door?

A house is shown with a banner over the garage door. The garage door is marked 16 ft wide and 12 ft high.
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Chi is planning to put a path of paving stones through her flower garden, as shown below. The flower garden is a square with side 10 feet. What will the length of the path be?

A square garden is shown that is marked 10’ on the side. There is a path of stones along the diagonal of the square.

14.1 feet

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Brian borrowed a 20 foot extension ladder to use when he paints his house. If he sets the base of the ladder 6 feet from the house, as shown below, how far up will the top of the ladder reach?

A house is shown with a ladder leaning against it. The ladder is marked 20’, and the distance from the house to the base of the ladder is marked 6’.
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Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is 85 feet and the width is 45 feet. What is the perimeter?

260 feet

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The length of a rectangle is 26 inches and the width is 58 inches. What is the perimeter?

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A rectangular room is 15 feet wide by 14 feet long. What is its perimeter?

58 feet

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A driveway is in the shape of a rectangle 20 feet wide by 35 feet long. What is its perimeter?

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The area of a rectangle is 414 square meters. The length is 18 meters. What is the width?

23 meters

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The area of a rectangle is 782 square centimeters. The width is 17 centimeters. What is the length?

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The width of a rectangular window is 24 inches. The area is 624 square inches. What is the length?

26 inches

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The length of a rectangular poster is 28 inches. The area is 1316 square inches. What is the width?

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Find the length of a rectangle with perimeter 124 and width 38.

24

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Find the width of a rectangle with perimeter 92 and length 19.

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Find the width of a rectangle with perimeter 16.2 and length 3.2.

4.9

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Find the length of a rectangle with perimeter 20.2 and width 7.8.

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The length of a rectangle is nine inches more than the width. The perimeter is 46 inches. Find the length and the width.

16 in., 7 in.

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The width of a rectangle is eight inches more than the length. The perimeter is 52 inches. Find the length and the width.

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The perimeter of a rectangle is 58 meters. The width of the rectangle is five meters less than the length. Find the length and the width of the rectangle.

17 m, 12 m

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The perimeter of a rectangle is 62 feet. The width is seven feet less than the length. Find the length and the width.

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The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.

13.5 m length, 12.8 m width

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The length of the rectangle is 1.1 meters less than the width. The perimeter of a rectangle is 49.4 meters. Find the dimensions of the rectangle.

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The perimeter of a rectangle is 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.

50 ft., 25 ft.

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The length of a rectangle is three times the width. The perimeter of the rectangle is 72 feet. Find the length and width of the rectangle.

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The length of a rectangle is three meters less than twice the width. The perimeter of the rectangle is 36 meters. Find the dimensions of the rectangle.

7 m width, 11 m length

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The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.

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The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.

160 yd., 120 yd.

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The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.

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A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.

85 ft., 40 ft.

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A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.

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Everyday math

Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?

24 feet

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Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a 50 foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 10 feet. How long can he make the other length?

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Writing exercises

If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.

area; answers will vary

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If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.

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Look at the two figures below.

On the left, we have a rectangle with height 2 and width 8. On the right, we have a square with height 4 and width 4.


Which figure looks like it has the larger area?
Which looks like it has the larger perimeter?
Now calculate the area and perimeter of each figure.
Which has the larger area?
Which has the larger perimeter?

Answers will vary.
Answers will vary.
Answers will vary.
The areas are the same.
The 2x8 rectangle has a larger perimeter than the 4x4 square.

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Write a geometry word problem that relates to your life experience, then solve it and explain all your steps.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has four rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “solve applications using triangle properties,” “use the Pythagorean Theorem,” and “solve applications using rectangle properties.” The rest of the cells are blank

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
Andrew Reply
divide 3x⁴-4x³-3x-1 by x-3
Ritik Reply
how to multiply the monomial
Ceny Reply
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin Reply

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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