Question

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

Answer 1

Diagonals d₁ and d₂ of the rhombus measure 120 m and 44 m, respectively.

Base of the parallelogram = 66 m

Now,
Area of the rhombus = Area of the parallelogram
$$\begin{gathered} \Rightarrow \frac{1}{2}\times d_1\times d_2=\mathrm{Base}\times \mathrm{Height} \\ \Rightarrow \frac{1}{2}\times 120\times 44=66\times \mathrm{Height} \\ \Rightarrow 60\times 44=66\times \mathrm{Height} \\ \Rightarrow 2640=66\times \mathrm{Height} \\ \Rightarrow \mathrm{Height}=\frac{2640}{66} \\ \Rightarrow \mathrm{Height}=40\mathrm{m} \end{gathered}$$

Hence, the measure of the altitude of the parallelogram is 40 m.