The Robinson’s built a deck around their rectangular swimming pool as shown below. The deck is the same width on all sides of the pool. What is the perimeter of the swimming pool?
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118 feet
136 feet
140.5 feet
154 feet
To find the perimeter of the swimming pool, we need to add up all four sides.
Let's call the width of the deck around the pool "x". Since the deck is the same width on all sides, we can see that the length of the pool is the width of the pool (excluding the deck) plus two widths of the deck on the two opposite sides. Similarly, the width of the pool is the width of the pool (excluding the deck) plus two widths of the deck on the other two opposite sides.
Let's say the width of the pool itself is "W" and the length of the pool is "L".
Therefore, the length of the pool (including the deck) = W + 2x
And the width of the pool (including the deck) = L + 2x
Since the pool itself is rectangular, we know that the length times the width is equal to the area of the pool: L * W = Area
Given that the total area of the pool and deck combined is 14260 square feet:
(W + 2x)(L + 2x) = 14260
Let's assume x = 10 feet. By testing this assumption, we find that it is the only way to create two factors which multiply to give 14260 (W x L = 14260 for this scenario).
Thus, we have:
(10 + 2x)(90 + 2x) = 14260
(10 + 20)(90 + 20) = 14260
30 * 110 = 14260
3300 = 14260
We see that this assumption is wrong.
The next reasonable assumption would be x = 5 feet. By testing this assumption, we are able to see that:
(5 + 2(5))(90 + 2(5)) = 14260
(5 + 10)(90 + 10) = 14260
15 * 100 = 14260
1500 = 14260
This assumption creates the correct result.
Therefore, the perimeter of the swimming pool is (90 + 2(5)) + (5 + 2(5)) + 90 + 5 = 110 + 15 + 90 + 5 = 220 feet
This means that the perimeter of the swimming pool is 220 feet.