Question

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the deck around the pool?

Answer 1

Let x ft wide is the deck around the pool.
then, length = (50 + 2x) ft
Breadth = (20 + 2x) ft
Now, area of deck = area of rectangular pool included deck - area of rectangular pool
⇒456= (50 + 2x)(20 + 2x) - 50 × 20
⇒456 = 100 + 100x + 40x + 4x² - 1000
⇒456 = 140x + 4x²
⇒ 114 = 35x + x²
⇒ x² + 35x - 114 = 0
⇒x² - 3x + 38x - 114 = 0
⇒x(x - 3) + 38(x - 3) = 0
⇒ x = 3 and -38
Hence, 3ft wide deck around the pool.