The length of a rectangle is 7 more than the width. The area is 60 square feet. Find the length and width of the rectangle.

Question

Math

Applications of quadratic equations

Answer 1

Let's start with the basics:

A = L x W

The problem states L = 7 + W. Let's substitute this into the equation:

A = (7 + W) x W

Now let's substitute in the area and simplify.

60 = W² +7W By combing the 60 on the other side, we have a quadratic equation we can solve.

W² +7W - 60 = 0 This format tells us that we need a number that will multiple to give a negative 60 but

has factors that when added will equal 7. The only ones that will give this is a -5 and

+12.

(W-5)(W +12) = 0 Now we will solve and will come up with two solutions.

W = 5 and W = -12 Because we can't have a negative area, the second solution is disregarded.

Therefore, the W = 5.

The Width is 5.

The Length is 7 +5, which is 12.

As a way to check this answer, multiplying 5 and 12 gives 60, which is the area stated in the problem.