# 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?

Jan 23, 2016

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

$P e r i m e t e r = l + w + l + w = 90 c m$ (Given)

$\implies 2 l + 2 w = 90$

$\implies 2 \left(l + w\right) = 90$

$\implies l + w = \frac{90}{2} = 45$

$\implies l + w = 45. \ldots \ldots \ldots . . \left(\alpha\right)$

Given that: Length is half of the width, i.e, $l = \frac{w}{2}$ put in $\alpha$

$\implies \frac{w}{2} + w = 45$

$\implies \frac{3 w}{2} = 45$

$\implies 3 w = 90$

$\implies w = 30 c m$

Since $l = \frac{w}{2}$

implies $l = \frac{30}{2} = 15$

$\implies l = 15 c m$

Hence, the length and width of the rectangle are $15 c m$ and $30 c m$ 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.