Question

if we assume that both figures have the same perimeter, then what is the value of x? x = 8 x = 6 x = 5 x = 7

Explanation:

Step1: Calculate perimeter of rectangle

The perimeter of a rectangle with length $l = 15$ and width $w=2x$ is $P_{rectangle}=2(l + w)=2(15 + 2x)=30 + 4x$.

Step2: Calculate perimeter of trapezoid

The perimeter of a trapezoid with sides $a = 10$, $b = 13$, $c = 2.5x$, $d = 2.5x$ is $P_{trapezoid}=10 + 13+2.5x+2.5x=23 + 5x$.

Step3: Set perimeters equal

Since $P_{rectangle}=P_{trapezoid}$, we have the equation $30 + 4x=23 + 5x$.

Step4: Solve for x

Subtract $4x$ from both sides: $30=23 + 5x-4x$. Then $30=23 + x$. Subtract 23 from both sides: $x=30 - 23=7$.

Answer:

$x = 7$