One side of a rectangle is 6 yd longer than three times another side. the area of the rectangle is 72 yd2. find the length of the longer side.

18 yds

Step-by-step explanation:

Let the length and width be L and W respectively.

Then L· W = area = 72 yd², so that L = (72 yd²) / W.

But also L = 3W + 6 yd.  Subbing this into  L· W = area = 72 yd², we get:

(3W + 6) · W = 72, or

3W² + 6W - 72 = 0.  Since all  four terms are evenly divisible by 3, we get:

W² + 2W - 24 = 0, which factors as follows:

(W + 6)(W - 4) = 0.  Then W + 6 = 0, or W = -6 (makes no sense for a length), and W - 4 = 0 yields W = 4 yds.

If the shorter side is of length 4 yds, then the longer side is of length

L = 3(4 yds) + 6 yds = 18 yds

18 yd

Step-by-step explanation:

(3x + 6) * x = 72

Use the distributive property

3x^2 + 6x = 72

3x^2 + 6x - 72 = 0

3(x^2 + 2x - 24) = 0

X^2 + 2x - 24 = 0

X can equal -6 and 4.

4 only works for this problem

4 * 3 = 12

12 + 6 = 18

So, the answer is 18 yd.

Let’s check our work.

3 * 4 = 12

12 + 6 = 18

18 * 4 = 72

So, we know for a fact that the longer side is 18 yd long.

I hope I helped!

Let me know if you need anything else!

~ Zoe