[Math] The perimeter of a rectangle is $48$ m and its area is $135$ m$^2$. Determine the sides of the rectangle.

Question

The perimeter of a rectangle is $48$ m and its area is $135$ m$^2$. Determine the sides of the rectangle.

I tried the following:

Perimeter $=48$ m
Let the length be $x$ m and the breadth be $y$ m

As we know, Perimeter $=2(x+y)=48$
$\Rightarrow x+y=24$ $[\cdots (1)]$
Area$=135$ m$^2$.
As we know, Area$=lb$
Therefore, $135$ m$^2$ $=xy$ $[\cdots (2)]$

But, how do I solve this?

Answer 1

$(x-y)^2=(x+y)^2-4xy=(24)^2-4.135=576-540=36$

Hence, $(x-y)=6$

Can you take it from here?