Question

Find the length of a side of a square, whose area is equal to the area of the rectangle with sides 240m and 70m.

Answer 1

Hint – In this question we have been given dimensions of a rectangle and we have to find the side of a square whose area is equal to that of the given rectangle. Use the basic formula for the area of the rectangle and equate it with that of the square to find out the side of the square.

Complete step-by-step answer:
Given data
Sides of rectangle are 240 m and 70 m
Let, length (L) = 240 m.
Breadth (B) = 70 m.
Now as we know that the area (A) of the rectangle is length multiplied by breadth.
$ \Rightarrow {A_r} = L \times B$
$ \Rightarrow {A_r} = 240 \times 70{\text{ }}{{\text{m}}^2}$.
Now it is given that the area of the square is equal to the area of the rectangle.
Let the area of the square be$\left( {{A_s}} \right)$.
$ \Rightarrow {A_s} = {A_r}$
$ \Rightarrow {A_s} = 240 \times 70{\text{ }}{{\text{m}}^2}$………………. (1)
Now as we know that the area of the square is equal to square to side of square.
Let the side of the square be x meter.
$ \Rightarrow {A_s} = {x^2}{\text{ }}{{\text{m}}^2}$………………………….. (2)
Now from equation (1) and (2) we have,
$ \Rightarrow {x^2} = 240 \times 70$
Now take the square root we have,
$ \Rightarrow x = \sqrt {240 \times 70} = \sqrt {8 \times 3 \times 10 \times 7 \times 10} = 20\sqrt {42} {\text{ m}}$.
So the side of the square is $20\sqrt {42} {\text{ m}}$.
So, this is the required answer.

Note – Whenever we face such types of problems the key concept involved is simply regarding the understanding of the basic formula for the area of sections like square and rectangle. Use this concept along with the information provided in the question to get the answer.