Question

The perimeter of a rectangle of sides $24$ cm and $16$ cm is equal to the perimeter of a square. Find the side and area of the square.

Answer 1

Step 1: Find the perimeter of rectangle.

Given : Length $=24$ cm and Breadth $=16$ cm

Perimeter of a rectangle $=2✕$ (length $+$ breadth)

$$\begin{gathered} =2(24+16) \\ =2✕40 \\ =80\text{m} \end{gathered}$$

Step 2: Find the side of square.

Since, Perimeter of given rectangle is equal to the perimeter of square.

And perimeter of square $=4\times$side

$$\begin{gathered} \Rightarrow 80=4✕\text{side} \\ \Rightarrow \left(\frac{80}{4}\right)=\text{side} \\ \Rightarrow 20\text{m}=\text{side} \end{gathered}$$

Step 3: Find the area of square.
Area of square $={\left(\text{side}\right)}^2$

$$\begin{gathered} ={\left(20\right)}^2 \\ =400{\text{m}}^2 \end{gathered}$$

Hence, side of square is $20\text{m}$and area of square is $400{\text{m}}^2$.