Question

abcd is a trapezoid.
if ac = 5x - 7 and bd = 2x + 8, find the value of x so that abcd is isosceles

Explanation:

Step1: Recall rhombus diagonal property

In a rhombus, diagonals are equal in length.

Step2: Set diagonals equal

$3x - 7 = 2x + 8$

Step3: Solve for $x$

Subtract $2x$ from both sides: $3x - 2x - 7 = 8$ → $x - 7 = 8$
Add 7 to both sides: $x = 8 + 7 = 15$

Answer:

15