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Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Shawn has $15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. How much should she invest in each account if she wants to earn 4.05% annual interest on the total amount?
$12,500 at 4.5%, $2,500 at 1.8%
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)
Solve Applications Using Triangle Properties
In the following exercises, solve using triangle properties.
The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.
The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of two sides are 19 feet and 14 feet. How long is the third side?
A triangular road sign has base 30 inches and height 40 inches. What is its area?
600 square inches
What is the height of a triangle with area 67.5 square meters and base 9 meters?
One angle of a triangle is more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
One angle of a right triangle measures What is the measure of the other angles of the triangle?
The measure of the smallest angle in a right triangle is less than the measure of the next larger angle. Find the measures of all three angles.
The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.
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 missing side. Round to the nearest tenth, if necessary.
In the following exercises, solve. Approximate to the nearest tenth, if necessary.
Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire?
Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?
Solve Applications Using Rectangle Properties
In the following exercises, solve using rectangle properties.
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