Question

A field in the form of a rhombus has each side of length 64 m and altitude 16 m. What is the side of a square field which has the same area as that of a rhombus?

Answer 1

$$\begin{gathered} \text{Given:} \\ \text{Each side of a rhombus shaped field = 64 m} \\ \text{Altitude = 16 m} \\ \text{We know: Area of rhombus = Side×Altitude} \\ \therefore \mathrm{A}{\text{rea of the field = 64×16=1024 m}}^2 \\ \text{Given: Area of the square field = Area of the rhombus} \\ {\text{We know: Area of a square=(Side)}}^2 \\ \therefore {\text{1024=(Side)}}^2 \\ \Rightarrow \text{Side=}\sqrt{1024}\text{=32 m} \\ \text{Thus, the side of the square field is 32 m.} \end{gathered}$$