Question

There is only a square whose perimeter and area are the same. What is the length of each side of this square?

Answer 1

Hint: First, we will assume the length of the sides of the square as x. Then we will find the perimeter of square and area of square. We will compare these two equations and from this we will find the length of each side of the square.

Complete step by step solution:
Here, we will draw a figure of square with all sides as x.

Now, we know that perimeter of square is summation of all the sides which is written in mathematical form as
Perimeter $=x+x+x+x=4x$ ………………………………(1)
Now, we have to find area of square which is given as
$area=side\times side=\left( x\times x \right)={{x}^{2}}$ …………………(2)
Now, in the question we are given that perimeter and area are equal. So, we will compare equation (1) and equation (2). By comparing, we will get
$perimeter=area$
On substituting the values, we get
$4x={{x}^{2}}$
Now, we will divide both sides with x. So, we will get
$4=x$
Thus, we can write it as $x=4$ .
So, the length of each side of the square is 4 units.

Note: Sometimes students make mistakes in perimeter and area i.e. instead of adding all the sides and finding the perimeter of square students take perimeter as 1 unit. So, the perimeter will be 1 instead of adding all the sides and the area will be ${{1}^{2}}=1$ . Thus, both perimeter and area are equal. This is a misconception students faced sometimes. So, do not make these silly mistakes.