A 174footlong fence is being placed around the perimeter of

A 174-foot-long fence is being placed around the perimeter of a rectangular swimming pool that has a 3-foot-wide sidewalk around it. The actual swimming pool without the sidewalk is twice as long as it is wide. Find the dimensions of the pool without the sidewalk.

Solution

Let the width of the swimming pool be x ft.. Then, its length is 2x. In cluding the sidewalk on both sides, the length becomes 2 x + 2*3 i.e. 2x + 6. The description can be seen in the following drawing. Then, the perimeter of the swimming pool ( including the sideqalk is 2( 2x+6) + 2x = 174 ( as 174 ft long fencing suffices for the pool inclund the sidewalk) Thus, 4x + 12 + 2x = 174 or, 6x = 174 -12 = 162 so that x = 162/6 = 27. Then, 2x = 2*27 = 54ft > Thus, the swimming pool ( without the sidewalk) is 27 ft. wide and 54 ft. long.