Answer:
$340
Step-by-step explanation:
The pool is 5 yards wide by 10 yards long, so adding the deck will make the total area 7 yards wide by 12 yards long, or ...
(7 yd)·(12 yd) = 84 yd^2
The pool itself is ...
(5 yd)·(10 yd) = 50 yd^2
so the area of the deck is ...
84 yd^2 -50 yd^2 = 34 yd^2
Wood for each of those square yards costs $10, so the total cost is ...
($10/yd^2)·(34 yd^2) = $340
Given:
Rectangular pool with dimensions = [tex]15[/tex] feet × [tex]30[/tex] feet
Width of the wooden deck to be built around the pool = [tex]3[/tex] feet
Cost of the lumber used for the deck = $[tex]10[/tex] per square feet
To Find:
Cost of the wood for the deck.
Solution:
In this question, we will find the area of the wood used to build the deck first then the cost to build the deck can be calculated by using the formula,
Cost of the wood for the deck = Area of the deck × Cost of the wood
Area of the rectangular (inner rectangle) pool = Length × width
= 15 × 30
= 450 square feet
Width of the deck = 3 feet
Therefore, length of the outer rectangle = 30 feet + [2×(3)] feet
= 36 feet
Similarly, width of the outer rectangle = 15 + [2×(3)]
= 21 feet
Area of the outer rectangle = Length × Width
= 36 × 21
= 756 square feet
Area of the wooden deck = Area of the outer rectangle - Area of the inner rectangle
= 756 - 450
= 306 square feet
Now cost of the wood used for the deck = 306 × 10
= $3060
Therefore, cost of the wood used for the deck around the pool will be $3060
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