Question

A boy walked along two adjacent sides of a rectangular field. If he had walked along the diagonal, then he would have saved a distance equal to one-fourth of the larger side. The ratio of the smaller to the larger side is:

विकल्प

• 7 : 24

• 11 : 18

• 24 : 7

• 18 : 11

Answer 1

7 : 24

Explanation:

Let, ABCD is a rectangle, with length `l` and breadth ‘b’

Distance travelled along two adjacent sides = `l + b`

Distance travelled along diagonal = `sqrt(l^2 + b^2)`

`(l + b) - (sqrt(l^2 + b^2)) = 1/4 l`  .....(Given)

⇒ `l + b - 1/4 l = sqrt(l^2 + b^2)`

⇒ `3/4 l + b = sqrt(l^2 + b^2)`

Squaring both sides,

⇒ `9/16 l^2 + b^2 + 2 xx 3/4 l xx b = l^2 + b^2`

⇒ `9/16 l^2 + b^2 + 3/2 lb = l^2 + b^2`

⇒ `3/2 lb = l^2 - 9/16 l^2`

⇒ `3/2 lb = (7l^2)/16`

⇒ `3/2 b = 7/16 l`

⇒ `b/l = 7/16 xx 2/3 = 7/24`

∴ `b : l` = 7 : 24