How many lighting fixtures does he need?

Question

Mr. Sanchez is installing inground lighting fixtures every 30 inches around the perimeter of his swimming pool. His swimming pool is in the shape of a rectangle with dimensions 15 feet by 20 feet. How many lighting fixtures does he need?

Answer 1

The question says he's installing the lights around the perimeter, so we start by calculating the perimeter of the pool. The perimeter of a rectangle is:

P = 2 l + 2 w

= 2(15) + 2(20)

= 30 + 40

= 70 ft

Mr. Sanchez has to have enough lights for 70 feet of perimeter. To find the number of lights needed for this distance, we just divide 70 feet by 30 inches, but first we need both of them to be in the same units. 30 inches in feet is 30/12 = 2.5 feet. Now we can divide:

70 / 2.5 = 28

Mr. Sanchez needs 28 lighting fixtures.

Answer 2

15 feet by 20 feet is equal to 180 inches by 240 inches.
 
That means there are 7 lights in one direction and 9 lights in the other direction.  Now, be very careful when counting, because the "corners" are counted both ways (so the perimeter is 6+8+6+8):

 

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