Question

The length of a rectangular garden is 3 yards greater

than the width of the garden. If the garden measures
15 yards diagonally, what is its length?

Answer 1

12

Explanation:

Let's call the width x and the length x + 3. Using the Pythagorean Theorem we can write:

(x + 3)² + x² = 15²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

2(x² + 3x - 108) = 0

2(x + 12)(x - 9) = 0

x + 12 = 0 or x - 9 = 0

x = -12 or x = 9

x cannot be -12 because length/width can't be negative so x = 9 which means that the length is 9 + 3 = 12.