The length of a rectangle is 7 centimeters less than its width. WHat are the dimensions of the rectangle if its are is 78 square centimeters?

Question

The length of the rectangle is ___ cm.

The width of the rectangle is ___ cm.

Answer 1

Hey!

So since we're looking for an area that involves two things (length and width), we need a way to define those two things based on what we've been given!

Let's let w = width and l = length. They can be defined (using the key word "less than") as such:

l = w - 7

w = w. (respectively)

Since we have two things in terms of one variable, w, let's set up an equation to find area! This is always l x w for rectangles, so we have:

l x w =

(w-7)(w) = 78.

Multiply this out, solve for w (width). You will end up with a quadratic equation that is factorable! REMEMBER dimensions aren't negative in the real world!

That will also give you enough info to go back and figure out what length is! Hope this helps.

Answer 2

length (l) = w - 7

area = l * w = 78

(w-7) * w = 78

w^2 - 7w - 78 = 0

(w-13)(w + 6) = 0

w = 13

l = 6