Question

A trapezoid has an area of 900 square meters. The height of the trapezoid is 40 meters (m), and

the length of the longer base is twice that of the shorter base. Find the length of each base of the trapezoid.

Answer 1

Check the picture below.

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}`