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?
Solution:
Given:
Each side of a rhombus shaped field $=64 \mathrm{~m}$
Altitude $=16 \mathrm{~m}$
We know: Area of rhombus $=$ Side $\times$ Altitude
$\therefore$ Area of the field $=64 \times 16=1024 \mathrm{~m}^{2}$
Given: Area of the square field $=$ Area of the rhombus
We know: Area of a square $=(\text { Side })^{2}$
$\therefore 1024=(\text { Side })^{2}$ $\Rightarrow$ Side $=\sqrt{1024}=32 \mathrm{~m}$
Thus, the side of the square field is $32 \mathrm{~m}$.