Question

The two parallel sides and the distance between them are in the ratio 3 : 4 : 2. If the area of the trapezium is 175 cm2; find its height.

Answer 1

Let the two parallel sides and the distance between them be 3x, 4x, 2x cm respectivley

$\therefore$ Area $=\frac{1}{2}$ (sum of parallel sides) $\times$ (distance between parallel sides)

$=\frac{1}{2}(3x+4x)\times 2x=175$ (given)

$\Rightarrow 7x\times x=175\Rightarrow 7x^2=175$

$\Rightarrow x^2=25\Rightarrow x=5$

$\therefore$ Height i.e. distance between parallel sides $=2x=2\times 5=10$ cm