Question

If the perimeter of a rectangle is 46 cm and the area is 132 square cm, then what are the dimensions of the rectangle?

Answer 1

Length = `12cm`
Breadth = `11cm`

Explanation:

You can use two variables and then simultaneous equations, or use one variable to define the length and the breadth.

I prefer to use one variable because we know the relationship between the length and the breadth,

If `P= 2(l+b) = 46`, then `l+b = 23`

If we let the breadth be `x` then the length is `23-x`

The area is `132 cm^2`

`A = l xx b rarr" " x(23-x) = 132`

`23x-x^2=132`

`x^2 -23x +132 =0" "larr` make the quadratic =0

To factorise, find factors of `132` which add to `23`

`(x-12)(x-11)=0`

`x=12 or x=11`

These are the required dimensions of the rectangle,

Check: `P= 2(12+11) = 2(23)=46cm`

`A= 12xx11 =132cm^2`