The length of a rectangle is 5 feet longer than it is wide. If each side is increased 5 feet, then the area is multiplied by 2. What was the size of the original rectangle?

Question

The length of a rectangle is 5 feet longer than it is wide. If each side is increased 5 feet, then the area is multiplied by 2. What was the size of the original rectangle?

Answer 1

Express the length and the width with variables: I am going to take the width before increase to be x; therefore, the length would be 5 feet longer, or x+5. Area=width × length = x(x+5)

After increase of of each side by five, the new length and width will be (add five to each of the previous designations: new width=x+5, and new length=x+5+5=x+10. The new area=(x+5)(x+10).

Since the new area is said to be twice old area, we write: (x+5)(x+10) = 2[x(x+5)]. We can safely cross out the (x+5) term from both sides of this equation [since this terms cannot be zero.] Therefore, you're left with:

x+10=2x, which gives you x=10.

You can check it by plugging it back: old area is 150 and new area is 300, which matches.

Best,

Tomaj