Question

If a storm window has an area of 400 square inches, what are the dimensions if the window is 12 inches higher than it is wide?

Answer 1

`14.88061 xx 26.88061` (Approximately)

Explanation:

Let `h` be the height and `w` be the width (both in inches).

Since `"Area" = "Height" xx "Width"`

`hxxw = 400`

Further we are told that
`h=w+12`

Therefore
`(w+12)xxw=400`

`rArr w^2+12w-400=0`

We can then apply the quadratic formula:
`color(white)("XXX")w= (-b+-sqrt(b^2-4ac))/(2a)`

To get
`color(white)("XXX")w=(-6+sqrt(12^2-4 * 1 * 400))/(2 * 1)`
(we can ignore the negative on the square root since `w>=0`)
`color(white)("XXX")~~14.88061`

and since `h=w+12`
`color(white)("XXX")h=26.88061`