Please help with this geometry question, this is urgent!!!!!!!! Best answer gets 10 points!!!?

Question

I have no idea how to do this, so please explain how you did it!

"You are building a swimming pool in the shape of a circle with a diameter of 28 feet. You also need a deck around the pool that is uniform in width. If the area of the deck is 60(pi sign) square feet, what is the width of the deck?

Thanks, for any help!!!!!!!

Answer 1

You need to get the area of the pool and the area of the deck, and add them to get the area of the whole thing (pool + deck) . If w is the width of the deck then the radius of the whole thing is (w + 14) since 14 is the radius of the pool.  Area = pi r squared so

whole area: π(14+w)(14+w) = &pi(196 + 28w + w^2)

pool only: π(14)(14) = 196π

deck: 60&pi

so since all terms have pi in them, divide all by pi.  Now you just have

196 + 28w + w^2 = 196 + 60

subtract 196: 28w + w^2 = 60

write in standard form: w^2 + 28w - 60 = 0

reverse FOIL: (w+30)(w-2) = 0

so w = -30 [impossible] or w = 2