Question

A rectangular rug has side lengths of (x- 2) feet
space does it cover?
and (x + 3) feet. How much floor space does it cover

Answer 1

Hi!

Your answer is $x^2+x+6$

We are asked to find the floor space it covers, which we can solve for by finding the area of the rectangular rug, given its dimensions.

Dimensions:

(x - 2) x (x + 3)

Area of a rectangle:

Length x Width = Area

Plug dimensions into the formula:

$(x - 2)(x +3)$

Use the Distributive Property and FOIL method to solve (if you are not familiar with the FOIL method, see the image attached below):

$x^2+3x-2x-6$

Combine like terms:

$x^2+x-6$

Now, this isn't a numerical value, but as we do not know the value of x, this is the simplest answer we can get.