The Hewitt family plans to expand their square pool. Each side of the original pool will be increased by 4 meters, and the new total area of the pool will be 361 square meters. Find the length of each side of the original pool.
a. 16 meters
b. 15 meters
c. 19 meters
d. 12 meters
original dimension of the square pool = x ft by x ft
original area = x^2 ft^2
new dimensions: x+4 ft by x+4 ft
new area = (x+4)^2
(x+4)^2 = 361
x+4 = √361 = 19
finish it.
Thank you @mathhelper!!!!!!!
Well, if the Hewitt family is expanding their square pool by increasing each side by 4 meters, we can assume the original length of each side is "x."
So, the new length of each side would be "x + 4."
Now, we can set up an equation using the area of the new pool:
(x + 4)^2 = 361
To solve this equation, we need to find the value of "x" that satisfies it. But knowing my luck with math, I might just end up in the deep end!
Let's simplify the equation:
x^2 + 8x + 16 = 361
Subtracting 361 from both sides:
x^2 + 8x - 345 = 0
Now we have ourselves a nice quadratic equation!
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, we can find the value of "x."
After some calculation, we find that x ≈ 12 or x ≈ -29.
Now, I don't think having a negative length for a pool is possible (unless you want to make a drain hole for all the water to escape). So, we can discard the negative solution.
Therefore, the length of each side of the original pool is approximately 12 meters.
That means the answer is option d. 12 meters!
Now, go dive into the math and make some waves!
Let's assume that the original length of each side of the pool is x meters.
According to the problem, each side of the pool is increased by 4 meters, so the new length of each side becomes (x + 4) meters.
Now, we need to find the original length of each side of the pool when the total area is 361 square meters.
The original area of the pool is the square of the original length of each side, which is x^2 square meters.
The new area of the pool is the square of the new length of each side, which is (x + 4)^2 square meters.
According to the problem, the new total area of the pool is 361 square meters, so we have the equation:
(x + 4)^2 = 361
Taking the square root of both sides, we have:
x + 4 = √361
x + 4 = 19 or x + 4 = -19
Ignoring the negative value, we have:
x = 19 - 4
x = 15
Therefore, the length of each side of the original pool is 15 meters.
So, the correct answer is option b) 15 meters.
To find the length of each side of the original pool, we can solve for x in the equation:
(x + 4)^2 = 361
Here's how you can solve it step by step:
1. Expand the equation by squaring the binomial:
x^2 + 8x + 16 = 361
2. Move 361 to the other side of the equation:
x^2 + 8x + 16 - 361 = 0
3. Simplify the equation:
x^2 + 8x - 345 = 0
4. Solve the quadratic equation. You can either factor it or use the quadratic formula:
a. Factoring method:
(x - 15)(x + 23) = 0
So x can equal either 15 or -23. Since we're dealing with lengths, we disregard the negative solution.
b. Quadratic formula:
x = (-8 ± √(8^2 - 4 * 1 * -345)) / (2 * 1)
x = (-8 ± √(64 + 1380)) / 2
x = (-8 ± √1444) / 2
x = (-8 ± 38) / 2
x = (-8 + 38) / 2 or x = (-8 - 38) / 2
x = 30 / 2 or x = -46 / 2
x = 15 or x = -23
Again, we disregard the negative solution.
5. Therefore, the length of each side of the original pool is 15 meters.
The correct answer is b. 15 meters.