Question

one side of a square was shortened by 3 inches and the other side was lengthened by 5 inches the are of the new rectangle is 55 square inches greater than half of the are of the original square. Find the length of the side of the original square

Answer 1

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) = 648*8 = 6464=64 Check!

Explanation: