Question

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

Answer 1

Given: Length of each side of rhombus $\left(b\right)=64m$

Altitude of rhombus $\left(h\right)=16m$

Now, Area of rhombus field $=$ Side $\times$ Altitude

$=64\times 16$

$=1024m^2$

It is given that area of square field $=$ Area of rhombus field

$\Rightarrow a^2=1024$[where $a=$ side of square field]

$\Rightarrow a=\sqrt{1024}$

$\Rightarrow a=\sqrt{4\times 4\times 8\times 8}$

$\Rightarrow a=4\times 8$

$\Rightarrow a=32$

$\therefore$ Side of square field $=32m$