Question

A square and rectangle have equal areas. The length of the rectangle is five inches more than twice the side of the square. The width of the rectangle is 6 inches less than the side of the square. Find the length of the side of the square.

Answer 1

Just to make things easier, imagine that x is the length of the side of the square:

According to the information, we can conclude that:

2x + 5 (inches) is the length of the rectangle.

x - 6 (inches) is the width of the rectangle.

Since the areas of the square and the rectangle are the same, we know that:

(2x + 5)(x - 6) = x²

2x² - 12x + 5x - 30 = x²

2x² - 12x + 5x - x² = 30

x² - 7x - 30 = 0

x² + 3x - 10x - 30 = 0

x(x + 3) - 10(x + 3) = 0

(x - 10) (x +3) = 0

Now we can slove each part independently:

x - 10 = 0 or x + 3 = 0

x = 10 or x = -3

Since the length of the side of the square can't be a negative number, we can cancel -3 out and keep 10 only.

So the length of the side of the square is 10 inches.

(This is how I usually do to solve problems of this kind)