Question

A square painting has a diagonal of 44 in. Lorraine wants to frame the picture.

Answer 1

124 inches of a frame is the required amount. 31 times 4 is 124.

Answer 2

Since it is a square we can use the rules for a 45-45-90 right triangle or Pythagorean Theorem to solve.
Using 45-45-90 rules:
When you cut the square down the diagonal you create a 45-45-90 right triangle with the hypotenuse = 44 in.
The rule is: hyp = sqrt2 * leg
                    44 = sqrt2 * leg
Divide both sides by the square root of 2 to find the leg.
                     31 = leg
To find the perimeter of the square, the length needed to make a frame, multiply the length of the leg by 4.
31 * 4 = 124 in