the length of a rectangular pool is 2 feet longer than twice its width.if the pool measures 13 feet diagonally, what are the measurements of the length and width

Answer 1

Use Pythagorean Theorem:

a^2 + b^2 = c^2

length^2 + width^2 = diagonal^2

(2w + 2)^2 + w^2 = 13^2 Use given information

(4w^2 + 8w + 4) + w^2 = 169

5w^2 + 8w - 165 = 0

(5w + 33)(w - 5) = 0

w = -33/5 or w = 5

Use positive solution

length = 2w + 2

length = 2(5) + 2

length = 12

ANSWER: Width = 5 feet AND Length = 12 feet