Question

The length of a rectangle is half of its width. The perimeter of the rectangle is 90 cm. What are the dimensions of the rectangle?

Answer 1

Let `l` and `w` denote the length and width respectively.

`Perimeter=l+w+l+w=90 cm` (Given)

`implies 2l+2w=90`

`implies 2(l+w)=90`

`implies l+w=90/2=45`

`implies l+w=45............(alpha)`

Given that: Length is half of the width, i.e, `l=w/2` put in `alpha`

`implies w/2+w=45`

`implies (3w)/2=45`

`implies 3w=90`

`implies w=30 cm`

Since `l=w/2`

implies `l=30/2=15`

`implies l=15 cm`

Hence, the length and width of the rectangle are `15cm` and `30 cm` respectively.

However, I think that the longest side of a rectangle is considered as length and the smaller side is considered as width if this is true then the question is meaningless. Because here the largest side is considered as width and smaller side as length.