Question

A parallelogram and a square have the same area. If the sides of the square measure 40 m, and altitude of the parallelogram measures 25 m, find the length of the corresponding base of the parallelogram.

Answer 1

Area of a square = ${\mathrm{Side}}^2$
Area of the given square = ${40}^2$
= 1600 m²
Area of the square = Area of the parallelogram
∴ Area of the parallelogram = $1600{\mathrm{m}}^2$
Area of the parallelogram = $\mathrm{Base}\times \mathrm{Height}$
$$\begin{gathered} \Rightarrow 1600=\mathrm{Base}\times 25 \\ \Rightarrow \mathrm{Base}=\frac{1600}{25} \\ \Rightarrow \mathrm{Base}=64\mathrm{m} \end{gathered}$$

Therefore, the length of the corresponding base of the parallelogram is 64 m.