Question

Since rugs will only be $6 per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of 8 feet and a diagonal length of 17 feet. How much will the rug cost?

Answer 1

Explanation:

first we need to get the area of the rug she is going to get

since the rug is a rectangular shape with width and diagonal

using Pythagoras theorem to find the opposite

let

A: opposite. ,. B: adjacent,. C: hypotenuse

`{c}^(2) = {a}^(2) + {b }^(2)`

`{17}^(2) = {8}^(2) + {b}^(2)`

`{b}^(2) = {17}^(2) - {8}^(2)`

`b = \sqrt{ {17}^(2) - {8}^(2) } = 15`

now the area if the new rug is

length x width

`15 * 8 = 120 {feet}^(2)`

$6 for a square foot

for 120 square feet

120 x 6 = $720

final Answer

the rug will cost $720