Question

if the values of area and perimeter of a square are equal, then what will be the value of each side

Answer 1

Step-by-step explanation:

LET THE SIDE OF THE SQUARE =a

area of the square = a^2

perimeter of the square =4a

NOW ATQ ,

AREA OF THE SQUARE = PERIMETER OF THE SQUARE

=> a^2=4a

=> a =4 ( dividing a in both sides )

¤ SIDE OF THE SQUARE = 4

Answer 2

➤ Answer

• Side of square = 4units.

➤ Given

• Area of square is equal to perimeter of square.

➤ To Find

• The side of square.

➤ Step By Step Explanation

Given that the area of square is equal to perimeter of square.

We need to find the side of square.

So let's do it !!

Assumption

Let us consider the side of square be x.

Now ⤵

Area of square = x² and perimeter of square = 4x

By substituting the values

$:\longmapsto\tt4x = {x}^{2} \\ \\:\longmapsto\tt 4 = \cfrac{{x}^{2}}{x} \\ \\ \dag\boxed{ \tt{ \purple{ \cfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}}}} \\ \\ :\longmapsto\tt4 = {x}^{2 - 1} \\ \\ :\longmapsto\bf4 = x$

Therefore side of square = 4 units.

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➤ Proof

By substituting the value of x.

L.H.S. ⤵

➠ 4 × 4 = 16 units.

R.H.S. ⤵

➠ (4)² = 16 units.

Therefore, L.H.S. = R.H.S.

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