Question

in the rectangle below, $eg = 5x + 36$ and $qp = 10x - 14$. find $x$.

Explanation:

Step1: Set equal rectangle diagonals

$EG = QP$

Step2: Substitute given expressions

$5x + 36 = 10x - 14$

Step3: Rearrange to isolate $x$

$36 + 14 = 10x - 5x$

Step4: Simplify and solve for $x$

$50 = 5x \implies x = \frac{50}{5}$

Answer:

$x = 10$