Question

The perimeter of a rectangle is 42 cm and its area is 20 sq.cm. what is the sum of length and breadth? find the length and breadth?​

Answer 1

Answer:

Perimeter=2(l+b)=42.....eqn 1.

area=lb=20....eqn2.

a) sum of length and breadth=l+b=42/2=21cm(from eqn 1)

b)

lb=20

l=20/b

substituting this value in eqn 1:

2(20/b+b)=42

2((20+b^2))=42b

20+b^2=21b

b^2-21b+20=0

solve and get the value of b.

use l=20/b to get l.

Answer 2

Sum of length and breadth = 21

Length of the rectangle is 20 cm and breadth is 1 cm

Given:

The perimeter of rectangle = 42 cm

Area of the rectangle = 20 Sq cm

To find:

Sum of length and breadth

The length and breadth of the rectangle

Solution:

Let l and b be the length and breadth of the rectangle

From given data perimeter of the rectangle, 2(l+b) = 42

⇒ l + b = 21 _(1)  

Therefore, sum of length and breadth = 21

From given data Area of the rectangle, lb = 20 Sq cm

⇒ b = 20/l _ (2)

Substitute (2) in (1)

⇒  l + 20/l  = 21

⇒ $\frac{l^{2}+20 }{l} = 21$  

⇒ l² + 20 = 21 l

⇒ $l^{2} + 20 - 21 l= 0$  Now solve it to get $l$ and $b$  

⇒ $l^{2} - 21 l + 20= 0$

⇒ $l^{2} - 20 l - l + 20= 0$

⇒ $l(l- 20)- (l - 20)= 0$

⇒ $(l- 20)(l-1)= 0$  

⇒ l - 20 = 0             or          l - 1 = 0

    l = 20                                 l = 1

Since length of the rectangle is longest side we will take  $l = 20$  

Substitute l = 20 in (1)

⇒ 20 + b = 21  

⇒ b = 21 - 20 = 1

Therefore, length of the rectangle is 20 cm and breadth is 1 cm

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