Question

A rectangle is 81 m long and 36 m broad.find the side of a square whose area is equal to the area of this rectangle

Answer 1

First area of rectangle:
length*breadth=81*36
=2916 m square

Area of square= side*side= 2916 m square
Side = 54 m

Answer 2

Given

Sides of rectangle

length= 81m

Breadth= 36m

Area of rectangle= Area of square

To Find

We have to find out the side of square

Solution

first find the area of square

$\bullet\sf\ Area\ of\ square= (side)^2\\ \\ \bullet\sf\ Area\ of\ rectangle= length\times breadth\\ \\ \\ :\implies\sf\ (side)^2= \ell\times b\\ \\ \\ :\implies\sf\ \ (Side)^2= 81\times 36\\ \\ \\ :\implies\sf\ Side= \sqrt{81\times 36}\\ \\ \\ :\implies\sf\ Side= \sqrt{9\times 9\times 6\times 6}\\ \\ \\ :\implies\sf\ Side= 9\times 6\\ \\ \\ :\implies\sf\ Side= 54m\\ \\ \\ :\implies\underline{\boxed{\sf\ Side\ of\ square= 54m}}$

Verification:-

Area of square = Area of rectangle

→ 54×54= 81×36

→ 2916sq.m = 2916sq.m

LHS = RHS

Hence our answer is correct !