Question

. A rectangle and a square have the same perimeter 100 cm. Find the side of the square. If the rectangle has a breadth 2 cm less than that of the square. Find area of the rectangle.

621 cm sq

621 m sq

200 cm sq

200 m sq​

Answer 1

GIVEN THAT

A rectangle and square have the same

perimeter = 100 cm

The breadth of rectangle is 2cm less from

the side of square.

TO FIND

Side of the square.

Area of the rectangle.

FORMULA USED

Perimeter of rectangle = 2(L + B)

Perimeter of square = 4 × side

Area of rectangle = L × B

SOLUTION

Perimeter of square = 4 × side

=) 4 × side = 100

=) side = 100

4

So, side of the square is 25 cm

Now,

According to question, the breadth is 2 cm less

than the side of square.

=) (25 - 2) cm = 23 cm

So, the breadth of the rectangle is

23 cm

Then,

Perimeter of rectangle = 2(L + B)

➡️ 2(ʟ + 23) = 100

➡️ 2L + 46 = 100

➡️ 2L = 100 - 46

➡️ 2L = 54

➡️ L = 54

2

=) L = 27

So, the length of the rectangle is 27 cm

So, Area of rectangle = L × B

➡️ (27 × 23) cm²

➡️ 621 cm²

So, the area of rectangle is 621 cm²