Each side of a square is lengthened by 3 inches. The area of this new, larger square is 64 square inches.

Question

Find the length of a side of the original square.

Answer 1

Hello, thank you for taking the time to post your question!

I would start by taking the square root of 64 in order to find the side length. What’s nice is that it’s a perfect square so it ends up being

sqrt(64) = 8 inches for the side length of the new larger square

That means that the old square has a length of

8 – 3 = 5 inches

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The easiest way to do this is to note that √64 = 8, so the sides of the new square have to be 8 inches long. The original square had sides that were 3 inches shorter = 8 - 3 = 5 inches.

 

To solve it algebraically, let x = the length of the sides of the original square.  The new square has sides that are 3 inches longer = x+3.  The area of the new square is 64 inches:

 

Area = (x+3)(x+3)

 

64 = x² + 6x + 9

 

0 = x² + 6x - 55

 

Factors to:

 

0 = (x+11)(x-5)

 

x = -11 and 5.  Since we can't have side equal -11 inches, the original sides were 5 inches long.

 

Check:

(x+3)(x+3) = 64

(5+3)(5+3) = 64

8*8 = 64

64=64 Check!