You are building a concrete deck around a rectangular swimming pool. The pool is three times as long as it is wide. The deck will have a constant width of four feet. In order to have enough concrete, you have calculated the area of the deck to be 832 square feet.
What are the dimensions of the pool?
I really do not know how to do this. I am extremely confused and need help. If anyone could please help me that would mean a lot to me! I am stressing over this and confused. Again, I would appreciate help a lot! Thank you. Also, there are no answers or choices that come with this.
If the width of the pool is w, then the length is 3w.
So, the difference in area between the whole thing and just the pool is the area of the deck: 832
(w+8)(3w+8) - w(3w) = 832
w = 24
So, the pool is 24x72 feet
Check:
The pool+deck has area (24+8)(72+8) = 2560
The pool has area 24*72 = 1728
2560-1728 = 832
Wow, thank you so much! My parents aren't here to help me so you did so much! :) I understand how you did 3w and from there on it all made sense. If only I used variables. Thank you so much!
aw, shucks...
<scuff scuff>
No worries, I'm here to help! Let's break down the problem step by step.
1. Let's assume the width of the pool is W feet.
- Since the length of the pool is three times its width, the length would be 3W feet.
2. We know the deck has a constant width of 4 feet on each side of the pool.
- So, the length of the pool including the deck on both sides would be 3W + 2(4) feet = 3W + 8 feet.
- Similarly, the width of the pool including the deck on both sides would be W + 2(4) feet = W + 8 feet.
3. To find the dimensions of the pool, we need to subtract the deck width from the total dimensions of the pool and deck.
- The length of just the pool would be 3W + 8 feet - 2(4) feet = 3W feet.
- The width of just the pool would be W + 8 feet - 2(4) feet = W feet.
4. The area of the deck is given as 832 square feet.
- The area of the deck can be calculated as the product of the length and width of the deck: (3W + 8) * (W + 8).
- Since we have the area of the deck, we can set up an equation: (3W + 8) * (W + 8) = 832.
5. Now we have a quadratic equation that we can solve for W.
- Expanding and rearranging the equation, we get: 3W^2 + 32W + 64 = 832.
- Simplifying further: 3W^2 + 32W - 768 = 0.
6. We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring for simplicity.
- Factoring the equation, we need to find two numbers whose product is -768 and whose sum is 32. After some trial and error, the numbers are -24 and 32.
- Rewriting the equation using the factored form: (3W - 24) * (W + 32) = 0.
7. From this factored form, we have two possible solutions:
- Either 3W - 24 = 0, which implies 3W = 24, and W = 8.
- Or W + 32 = 0, which implies W = -32. Since width cannot be negative, we disregard this solution.
8. Therefore, the width of the pool is 8 feet, and the length of the pool is three times the width, which is 3 * 8 = 24 feet.
So, the dimensions of the pool are 8 feet (width) and 24 feet (length).