# Miguel wants to buy a new rug for his bedroom. He knows that the length is 2 feet more than the width, but can't remember either dimension.If the total area of the room is 90 square feet, what are...

Miguel wants to buy a new rug for his bedroom. He knows that the length is 2 feet more than the width, but can't remember either dimension.

If the total area of the room is 90 square feet, what are the dimensions of Miguel's room, to the nearest tenth of a foot?

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w = width

w + 2 = length

w(w + 2) = 90

w^2 + 2w -90 = 0

Probably the easiest way to solve this is to make a list of deminsions with a spreadsheet

Lenth Width Product 8.52 10.52 89.6304 8.53 10.53 89.8209 8.54 10.54 90.0116 8.55 10.55 90.2025So the width is about 8.54 ft and the length is about 10.54 ft.

Given that the length of the room is 2 feet longer than the width, and that the total area is 90 sq ft, find the dimensions to the nearest tenth of a foot.

(1) Let `w` be the width; then `w+2` would be the length.

(2) Area = length times width, so:

`90=w(w+2)`

(3) `w^2+2w-90=0` Using the qudratic formula we get:

`w=(-2+-sqrt(4-4(1)(-90)))/2`

`=(-2+-sqrt(364))/2`

`~~8.54 "or" 10.54`

**(4) Thus the dimensions to the nearest tenth of a foot are 8.5ftx10.5ft**