Question

Perimeter of a rectangleis 42 cm and its area is 20cm2. a) What is the sum of length and breadth? b) Find length and breadth?​

Answer 1

Given :-

♦ Perimeter of a rectangle is 42 cm.

♦ Area of the rectangle is 20 cm².

To find :-

♦ The sum of the length and breadth.

♦ Length of the rectangle.

♦ Breadth of the rectangle .

Solution :-

Let the length of the rectangle be l cm

Let the breadth of the rectangle be b cm

Perimeter of the rectangle = 2(l+b) cm

According to the given problem

Perimeter of the rectangle = 42 cm

=> 2(l+b) = 42

=> l+b = 42/2

=> l+b = 21 cm ---------------(1)

The sum of the length and breadth of the rectangle is 21 cm

Area of the rectangle = lb cm²

According to the given problem

Area of the rectangle = 20 cm²

=> lb = 20 ---------------------(2)

We know that

(a-b)² = (a+b)²-4ab

(l-b)² = (l+b)²-4lb

=> (l-b)² = (21)²-4(20)

=> (l-b)² = 441 - 80

=> (l-b)² = 361

=> l-b = ±√361

=> l-b = ± 19

=> l-b = 19 ----------------------(3)

Since, the length and breadth can't be negative.

On adding (1)&(3)

l+b = 21

l-b = 19

(+)

________

2l+0 = 40

________

=> 2l = 40

=> l = 40/2

=> l = 20 cm

On substituting the value of l in (1) then

=> 20+b = 21

=> b = 21-20

=> b = 1 cm

Length = 20 cm

Breadth = 1 cm

Answer :-

♦ The sum of the length and breadth of the rectangle is 21 cm

♦ The length of the rectangle = 20 cm

♦ The breadth of the rectangle = 1 cm

Used formulae:-

♦ Area of a rectangle = lb sq.units

♦ Perimeter of a rectangle = 2(l+b) units

• l = length
• b = breadth