Question

in parallelogram abcd below, bd = 38 and be = 8x + 59. solve for x.

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $BE = \frac{1}{2}BD$.

Step2: Substitute given values

Substitute $BD=38$ and $BE=8x+59$:
$8x + 59 = \frac{1}{2} \times 38$

Step3: Simplify right-hand side

Calculate $\frac{1}{2} \times 38 = 19$, so:
$8x + 59 = 19$

Step4: Isolate the variable term

Subtract 59 from both sides:
$8x = 19 - 59$
$8x = -40$

Step5: Solve for x

Divide both sides by 8:
$x = \frac{-40}{8}$

Answer:

$x = -5$