SOLUTION: the length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and width of the rectangle?

Question 5550: the length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and width of the rectangle?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Alright. We know that the area formula for a rectangle is length * width.
Let's call L the length and W the width.

The first sentence can be translated into L = 2 + W. However, we're going to rewrite that as L = W + 2. Why, you say? Because writing the term with the variable first looks better in writing.

Now, we know that A = L*W. The area is given to us as 80 m^2. But we can't have two unknowns here because that would give us an infinite number of solutions. We'll have to substitute W + 2 for the L so that we're only going to deal with one variable, which is W.

So, which we'll rewrite as just because it looks better.

So now we've got . We've got to distribute to get . However, we want to put the 80 with the other terms so that the right hand side of the equation will turn out to be 0. That way, we can find the solution to this quadratic equation. Now, we have .

I trust that you know how to factor polynomials and what the factors mean for the equation when you get them. .

Out of w + 10 and w - 8, w - 8 will be the factor that would give us a positive answer to w - 8 = 0. In this case, the answer is 8. We didn't pick the w + 10 because that would've given us a -10 for an answer, which is not a possible value for a length.

Alright. We're almost there. We know now that the width is 8. What about the length? The problem says that the length is 2 meters longer than the width. That would put the length at 10. So the width is 8 and the length is 10.
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