Question

The area of a rectangle is same as that of a circle of radius root35 by root11 cm. 8f the length of the rectangle exceeds its breadth by 3 cm, then the length of the rectangle is

The answer is 5cm.
Please give full explanation.

Answer 1

Let see your answer !!!!

Let the breadth be (x)cm. Then,

length = (x + 5)cm

Area = x × (x + 5)

= (x^2 + 5x)cm^2

New length = (x + 5 + 1)cm

= (x + 6)cm

New breadth = (x + 1)cm

New area formed = (x^2 + 5x + 34)cm^2

According to question ,

(x + 6) (x + 1) = x^2 + 5x + 34

=> x^2 + x + 6x + 6 = x^2 + 5x + 34

=> x^2 + 7x + 6 = x^2 + 5x + 34

=> x^2 - x^2 + 7x - 5x = 34 - 6

=> 2x = 28

=> x = 28/2

=> x = 14

Hence , breadth = 14cm

and length = (14 + 5)cm

= 19cm