Rectangles......

Question

The length of a rectangle is 4 inches longer than it is wide. If the area is 45 square inches, what are the dimensions of the rectangle?

Answer 1

Let's let the variable w represent the width of the rectangle and the variable l represent the length of the rectangle.

Since the length is 4 inches longer than the width, we can write:

l = 4 + w

Also area is equal to length times width, so we can write:

(4 + w) * w = 45 sq inches

This is equivalent to 4w + w^2 = 45 OR w^2 + 4w = 45

We can find possible values for w by solving:

w^2 + 4w = 45

w^2 + 4w - 45 = 0

The factors of this expression are: (w + 9) (w - 5) = 0

w can be -9 or 5

Since the width can not be a negative value , the width of the rectangle would be 5 inches.

The length would be 4 + w or 4 + 5 = 9 inches.