Question

the perimeter of a square is the same as the perimeter of the rectangle. if the rectangle is of size 105cm by 15cm,then find the area of the square.​

Answer 1

Answer:

3600cm^2

Step-by-step explanation:

see image for detailed solution

Answer 2

Concept :-

In the question, it is given that the perimeter of a square is same as the perimeter of the rectangle and the length and breadth of the rectangle is also given. From which we will calculate the side and then the area of the square. Step wise solution is given below.

Given :-

The perimeter of a square is = The perimeter of the rectangle

Length of the rectangle = 105 cm

breadth of the rectangle = 15 cm

Formula to be used :-

The perimeter of a square = 4 x side

The perimeter of the rectangle = 2(Length + Breadth)

Area of the square = $(side)^{2}$

Solution :-

The perimeter of a square is = The perimeter of the rectangle

=> 4 x side = 2(Length + Breadth)

[Substituting the formula of perimeter of both the figures]

=> 4 x side = 2(105 cm + 15 cm)

=> 4 x side = 2 x 120 cm

=> 4 x side = 240 cm

$=> side = \frac{240\: \:cm}{4} \\ \\ => side = 60 \: \:cm$

Now, we have calculated side and we will find the area from it.

Area of the square = $(side)^{2}$

$Area\: \: of\: \: the\: \: square = (60 \: \: cm)^{2} \\ \\ Area\: \: of\: \: the\: \: square = 3600 cm^{2}$

Answer :-

Area of the square is 3600 $cm^{2}$