Question

In the following figure, if the dimensions of the trapezoid are as shown and the area of the trapezoid is $144$, what is the value of $x$?

• A. $2$
• B. $3$
• C. $4$
• D. $6$
• E. $8$

Answer 1

The correct option is A $2$

Given, area of trapezoid $=144,h=4x,a=6x,c=12x$
We know, area of trapezoid is $A=\frac{h}{2}(a+c)$
$\Rightarrow 144=\frac{4x}{2}(6x+12x)$
$\Rightarrow 144=\frac{4x}{2}\left(18x\right)$
$\Rightarrow 288={72x}^2$
$\Rightarrow x^2=\frac{288}{72}=4$
$\Rightarrow x=2$