Question

The perimeter of an equilateral triangle and a square is the same. Find the area of the square if the perimeter of the triangle is 24 cm square

Answer 1

Answer :

The area of the square is 36 cm².

Clarification :

Here, we are given that the perimeter of an equilateral triangle and a square is the same and the perimeter of the triangle is 24 cm². In order to calculate the area of the square, firstly we need to find its side. Through the given enough information we'll find the side of the square and then substitute the values to find the area of the square.

Given :

• The perimeter of an equilateral triangle and a square is the same.

• Perimeter of the triangle is 24 cm².

To calculate :

• The the area of the square.

Calculation :

According to the question :

$\qquad$

$\star$ The perimeter of an equilateral triangle and a square is the same, that is :

$\rm {\longmapsto {Perimeter}_{(Equilateral \: \triangle)}= {Perimeter}_{(Square)}} \\ \\ \\ \rm {\longmapsto 3s= 4 \times Side} \\ \\ \\ \bf {\lgroup s = side \rgroup} \\ \\ \\ \rm {\longmapsto 24 \: cm = 4 \times Side} \\ \\ \\ \bf {\lgroup Perimeter (\triangle) = 24 \: cm \: (Given) \rgroup} \\ \\ \\ \rm {\longmapsto \dfrac{24}{4} \: cm = Side} \\ \\ \\ \longmapsto \boxed{\rm { 6 \: cm = Side}}$

Now, hence side of the square is 6 cm.

$\star$ Calculating its area :

$\rm {\longrightarrow {Area}_{(Square)} = Side \times Side}$

$\rm {\longrightarrow {Area}_{(Square)} = 6 \: cm \times 6 \: cm }$

$\longrightarrow \boxed{\rm { {Area}_{(Square)} = 36 \: {cm}^{2} }}$

Henceforth, area of the square is 36 cm².

Answer 2

∵ Perimeter of the equi. triangle = Perimeter of square,

∴ Perimeter of square = 24 cm

∵ Perimeter of square = 4(side),

If side of the sq. = (a),

So, 4a = 24

⇒ a = 6 cm

Now, area of sq. = (side)² = (a)² = (6 cm)² = 36 cm².

∴ The area of the square is of 36 cm².