Mensuration MCQ 1: (Carpet length and width ratio, area)

A. 4 : 3                      b) 8 : 7                  c)4 : 1                      d) 6 : 5

Solution:

We consider the shape of the carpet in two cases separately.

Case 1:

In the first case let the length and breadth of the carpet be in the ratio;

3x:2x

i-e if length = 3x then breadth = 2x

So by applying formula of perimeter of a rectangle which is;

\[ Perimeter Of Rectangle= 2(Length+Breadth) \]

So,

\[ Perimeter Of Carpet= 2(3x+2x)=10x \]

Case 2

In the second case we suppose that length and breadth are in the ratio;

7y:3y

i-e If length = 7y then breadth =3y

Again using perimeter formula;

\[ Carpet Perimeter = 2(7y+3y)=20y \]

But according to the question the perimeter does not change after amendments in length and breadth, so perimeters of both casese should be equal;

i-e

10x=20y

or

x=2y