# The area of a rectangle is #20# #cm^2#. The length is #8# more than the width. How do you find the width in cm?

##### 1 Answer

The width of the rectangle is

#### Explanation:

Let's first recall the formula for the area of a rectangle:

We can first substitute

Now what? We have two variables but how do we find either of them? Looking back at the question, we see that "the length is 8 more than the width." Voila! Now we can write the length in terms of the width! So now we can switch out

Now, using the Distributive Property, we can expand out the right side of the equation:

We can subtract

Now, we can use factoring to simplify this problem. So our task now is to find two factors of

We found our pair! 2 and -10 or -2 and 10! So now, we can write the quadratic equation in an

And since the product of

Now let's assume that

Now, we can see that