Suppose you want to build a rectangular sandbox where the width is 4 feet less than the length and the diagonal is 4 ft longer than the length what are the dimensions of the sandbox

Answer 1

This is a simple Pythagorean theorem question. We recognize that when a problem has a shape like a rectangle or a right triangle, we may have to apply this theorem. The most difficult part is assigning the variables to each side. Once we were able to convert the word problem into a picture, it simply becomes an algebra question. When solving for X, we know that 0 is not a possible answer. Therefore, we are left with 16 ft as our final length and can then find the width and diagonal by simply subtracting 4 and adding 4.

Answer 2

l2 + (l - 4)2 = (l + 4)2

l2 + l2 - 8l + 16 = l2 + 8l + 16

l2 - 16l = 0

l(l - 16) = 0

l = 0 ----> impossible

l - 16 = 0

l = 16 feet

16 - 4 = 12 feet