Question

A square has a side of $2x$ unit. Height and one of the parallel sides of a trapezoid measure $x\text{units}$. The other parallel side of the trapezoid is of length $10\text{units}$. If area of the square and the trapezoid are equal, then find the value of x?

• A. $\frac{20}{7}$ units
• B. $\frac{5}{7}$ unit
• C. $\frac{7}{10}$ unit
• D. $\frac{10}{7}$ units

Answer 1

The correct option is D $\frac{10}{7}$ units

Lets draw a trapezoid ABCD of the given dimensions.Given,
$BC=10\text{unit}$
$AD=x\text{unit}$
Height of the trapezoid $=x$ unit
AD is parallel to BC

As we know,
Area of a trapezoid $=\frac{1}{2}\times$ (sum of the parallel sides)$\times h$

$=\frac{1}{2}\times (BC+AD)\times DE$

$=\frac{1}{2}\times (10+x)\times x$

Area of square = side x side
$=2x\times 2x$
$=4x^2$

Given, the area of square and trapezoid are equal
So,

Area of the trapezoid = Area of the square

$\frac{1}{2}\times (10+x)\times x=4x^2$

$10+x=\frac{4x^2\times 2}{x}=8x$

$8x-x=10$

$x=\frac{10}{7}$ units

Option (d) is correct.