Question

use the diagram shown to the right to find the unknown lengths of sides. the perimeter of the trapezoid is 135 inches. the length of the sides measuring x in. is . (simplify your answer. type an integer or a decimal.) the length of the side measuring 2.5x in. is . (simplify your answer. type an integer or a decimal.) the length of the side measuring 4.5x - 9 in. is . (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a trapezoid is the sum of the lengths of its sides. So $P=x + x+2.5x+(4.5x - 9)$. Given $P = 135$.

Step2: Combine like - terms

$x + x+2.5x+4.5x-9=(1 + 1+2.5 + 4.5)x-9=9x-9$.

Step3: Set up equation and solve for x

Set $9x - 9=135$. Add 9 to both sides: $9x=135 + 9=144$. Then divide both sides by 9: $x=\frac{144}{9}=16$.

Step4: Find side lengths

For side length $x$, it is 16 inches.
For side length $2.5x$, substitute $x = 16$, we get $2.5\times16 = 40$ inches.
For side length $4.5x-9$, substitute $x = 16$, we get $4.5\times16-9=72 - 9=63$ inches.

Answer:

The length of the sides measuring $x$ in. is 16
The length of the side measuring $2.5x$ in. is 40
The length of the side measuring $4.5x - 9$ in. is 63