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

Given:
Each side of a rhombus shaped field = 64 m
Altitude = 16 m
We know: Area of rhombus = Side x Altitude
\[ \therefore  {\text{ Area of the field }= 64\times16=1024 m}^2 \]
Given: Area of the square field = Area of the rhombus
\[ {\text{ We know: Area of a square }=(\text{ Side })}^2 \]
\[ \therefore {1024=(\text{ Side })}^2 \]
\[ \Rightarrow\text{ Side }=\sqrt{1024}=32 m\]
Thus, the side of the square field is 32 m.