Question

The perimeter of the rectangle is 80 cm. The area of the rectangle is acm2 . (i) show that x 2 40x + a = 0.​

Answer 1

Proved

Explanation:

Given

`p = 80` ---- perimeter

`a \to area`

Required

`x^2 + 40x + a = 0`

The perimeter is calculated as:

`p = 2(x + y)`

Where

`x,y \to` the rectangle dimension

So, we have:

`2(x + y) = 80`

Divide by 2

`x + y = 40`

Make y the subject

`y = 40 - x`

The area of the rectangle is:

`a = xy`

`a = x * (40 -x)`

`a = 40x -x^2`

Equate to 0:

`x^2 - 40x + a = 0`