# 9.4 Use properties of rectangles, triangles, and trapezoids  (Page 5/17)

 Page 5 / 17

The area of a rectangle is $598$ square feet. The length is $23$ feet. What is the width?

26 ft

The width of a rectangle is $21$ meters. The area is $609$ square meters. What is the length?

29 m

The perimeter of a rectangular swimming pool is $150$ feet. The length is $15$ feet more than the width. Find the length and width.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. the length and width of the pool Step 3. Name. Choose a variable to represent it. The length is 15 feet more than the width. Let $W=\text{width}$ $W+15=\text{length}$ Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question. The length of the pool is 45 feet and the width is 30 feet.

The perimeter of a rectangular swimming pool is $200$ feet. The length is $40$ feet more than the width. Find the length and width.

30 ft, 70 ft

The length of a rectangular garden is $30$ yards more than the width. The perimeter is $300$ yards. Find the length and width.

60 yd, 90 yd

## Use the properties of triangles

We now know how to find the area of a rectangle. We can use this fact to help us visualize the formula for the area of a triangle. In the rectangle in [link] , we’ve labeled the length $b$ and the width $h,$ so it’s area is $bh.$

We can divide this rectangle into two congruent triangles ( [link] ). Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of each triangle is one-half the area of the rectangle, or $\frac{1}{2}bh.$ This example helps us see why the formula for the area of a triangle is $A=\frac{1}{2}bh.$

The formula for the area of a triangle is $A=\frac{1}{2}bh,$ where $b$ is the base and $h$ is the height.

To find the area of the triangle, you need to know its base and height. The base is the length of one side of the triangle, usually the side at the bottom. The height is the length of the line that connects the base to the opposite vertex, and makes a $\text{90°}$ angle with the base. [link] shows three triangles with the base and height of each marked.

## Triangle properties

For any triangle $\text{Δ}ABC,$ the sum of the measures of the angles is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

The perimeter of a triangle is the sum of the lengths of the sides.

$P=a+b+c$

The area of a triangle is one-half the base, $b,$ times the height, $h.$

$A=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}bh$

Find the area of a triangle whose base is $11$ inches and whose height is $8$ inches.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. the area of the triangle Step 3. Name. Choose a variable to represent it. let A = area of the triangle Step 4. Translate. Write the appropriate formula. Substitute. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question. The area is 44 square inches.

#### Questions & Answers

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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Sherica
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Sherica
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Tamia
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Uday
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Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Porter
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Porter
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Cesar
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
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Prasenjit
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Azam
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Prasenjit
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Damian
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Azam
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Uday
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Uday
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Prasenjit
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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