Question

I need help solving this question

Answer 1

Option B:

The value of x is $-\frac{11}{2}$.

Solution:

JKLM is an isosceles trapezoid.

JK and LM are legs which are congruent sides and KL is the base.

JK = 8x - 9, KL = 7x + 10 and LM = 10x + 2

By the definition of isosceles trapezoid:

⇒ JK = LM

$\Rightarrow 8x-9=10x+2$

Add 9 both sides.

$\Rightarrow 8x-9+9=10x+2+9$

$\Rightarrow 8x=10x+11$

Subtract 10x from both sides.

$\Rightarrow 8x-10x=10x+11-10x$

$\Rightarrow -2x=11$

Divide by -2 on both sides.

$\Rightarrow \frac{ -2x}{-2} =\frac{11}{-2}$

$\Rightarrow x = -\frac{11}{2}$

The value of x is $-\frac{11}{2}$.

Option B is the correct answer.