Question

A cement walkway of uniform width has been built around an in-ground rectangular pool. the area of the walkway is 1344 square feet. the pool itself is 80 feet long by 20 feet wide. what is the width of the walkway?

Answer 1

Answer:

6 feet.

Step-by-step explanation:

Dimensions of the Pool =80 feet long by 20 feet wide

Area of the walkway =1344 square feet.

If the width of the walkway=w

• Length of the Larger Rectangle =80+2w
• Width of the Larger Rectangle =20+2w

Area of the Walkway =Area of the Larger Rectangle - Area of the Pool

$1344=(80+2w)(20+2w)-(80*20)\\1344=80*20+160w+40w+4w^2-80*20\\4w^2+200w=1344\\4w^2+200w-1344=0\\We factorize\\4(w^2+50w-336)=0\\4(w^2-6w+56w-336)=0\\w(w-6)+56(w-6)=0\\(w-6)(w+56)=0\\w-6=0 or w+56=0\\w=6 ft or w=-56 \\Therefore, the width of the walkway , w=6 feet.$