Question

A rectangle is (x+2)cm long and 5cm wide. If a square of side x cm has the same perimeter as that of rectangle, what is the length of the side of the square?​

Answer 1

Answer:

4x = 2x + 14

2x=14

x=7 centimetres

Answer 2

Required Answer :

The side of the square = 7 cm

Given :

• Length of a rectangle = (x + 2) cm
• Breadth of a rectangle = 5 cm
• Side of the square = x cm
• Perimeter of rectangle is equal to the perimeter of square

To find :

• The length of the side of the square

Solution :

Firstly, we will calculate the perimeter of the rectangle by using the following formula.

• Perimeter of rectangle = 2(l + b)

where,

• l denotes the length of the rectangle
• b denotes the breadth of the rectangle

Substituting the given values :

→ Perimeter of the rectangle = 2(x + 2 + 5)

→ Perimeter of the rectangle = 2(x + 7)

→ Perimeter of the rectangle = 2x + 14

Therefore,

• The perimeter of the rectangle = (2x + 14) cm

Now, we will calculate the perimeter of the square by using the following formula.

• Perimeter of square = 4a

where,

• a denotes the side of the square

Substituting the given values :

→ Perimeter of the square = 4x

Therefore,

• The perimeter of square = (4x) cm

Now, according to the question :

→ Perimeter of rectangle = Perimeter of square

→ 2x + 14 = 4x

→ 14 = 4x - 2x

→ 14 = 2x

→ 14/2 = x

→ 7 = x

The value of x = 7

Therefore,

• The side of the square = 7 cm