Question

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m add 44 m. If one of the sides of the ∥gm is 66 m long, find its corresponding altitude.

Answer 1

Area of the rhombus$=\frac{1}{2}\left(\mathrm{Product}\mathrm{of}\mathrm{diagonals}\right)=\frac{1}{2}\left(120\times 44\right)=2640{\mathrm{m}}^2$

Area of the parallelogram$=\mathrm{Base}\times \mathrm{Height}=66\times \mathrm{Height}$

Given:
The area of the rhombus is equal to the area of the parallelogram.

$$\begin{gathered} \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 66\times \mathrm{Height}=2640 \\ \Rightarrow \mathrm{Height}=\frac{2640}{66}=40\mathrm{m} \end{gathered}$$

∴ Corresponding height of the parallelogram = 40 m