At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner diameter is 22yd and its outer diameter is 34yd. We are going to give a new layer of coating to the path. If one gallon of coating can cover 6yd2, how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for π.)

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step-by-step explanation:

step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4