Question

What is the dimensions of a rectangle with an area of 10 square feet if its length is 8 ft more than twice the width?

Answer 1

`10" ft."xx1" ft."`

Explanation:

Let the length be `L` feet
and the width be `W` feet

We are told
`color(white)("XXX")L=2W+8`

so the area, `A`, is
`color(white)("XXX")A=LxxW=(2W+8) * W = 2W^2+8W`
but we are also told that the area is `10" sq.ft."`

So
`color(white)("XXX")2W^2+8W=10`

`color(white)("XXX")W^2+4W=5`

`color(white)("XXX")W^2+4W-5=0`

`color(white)("XXX")(W+5)(W-1)=0`

`W=-5color(white)("xxx")"or"color(white)("xxx")W=1`

A negative length is not possible, so the only valid possibility is `W=1`

and, since `L=2W+8`
`color(white)("XXX")L=10`