The dimensions is 180 yards of fence should be purchased to enclose the deck.
To solve this problem, we can use the following steps:
Find the perimeter of the pool.
Find the perimeter of the fence.
Multiply the perimeter of the fence by the ratio of the dimensions of the fence to the dimensions of the pool.
Step 1: Find the perimeter of the pool.
The perimeter of a rectangle is equal to the sum of the lengths of its sides. Therefore, the perimeter of the pool is:
perimeter of pool = 2(length of pool) + 2(width of pool)
= 2(60 yards) + 2(30 yards)
= 120 yards + 60 yards
= 180 yards
Step 2: Find the perimeter of the fence.
The perimeter of the fence is equal to the sum of the lengths of its sides. Since the ratio of the dimensions of the fence to the dimensions of the pool is 1/3, the length of the fence is 3 times the length of the pool and the width of the fence is 3 times the width of the pool. Therefore, the perimeter of the fence is:
perimeter of fence = 2(length of fence) + 2(width of fence)
= 2(3 * length of pool) + 2(3 * width of pool)
= 6(length of pool) + 6(width of pool)
= 6(60 yards) + 6(30 yards)
= 360 yards + 180 yards
= 540 yards
Step 3: Multiply the perimeter of the fence by the ratio of the dimensions of the fence to the dimensions of the pool.
perimeter of fence * ratio of dimensions of fence to dimensions of pool = 540 yards * 1/3 = 180 yards
Therefore, 180 yards of fence should be purchased to enclose the deck.
Complete question:
The dimensions of the rectangular pool shown below are 60 yards by 30 yards. A fence will be built around the outside of the deck. The ratio of the dimensions of the pool to the dimensions of the fence is 1/3. How many yards of fence should be purchased to enclose the deck?
A. 270 yards
B. 540 yards
C. 200 yards
D. 312 yards