SOLUTION: I have already answered the question, I just want to check my work. A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. The distance along the ground

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Question 374277: I have already answered the question, I just want to check my work.
A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. The distance along the ground from the bottom of the pole to the end of the wire is 4 feet greater than the height where the wire is attached to the pole. How far up the pole does the guy wire reach?
x^2+(x+4)^2=20^2
x=12
Answer by sophxmai(62) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, this is correct.

The guy wire, the telephone phone and the ground form a right-angled triangle.
Your measurements are x, x+4, and 20.
To solve for x, you could use the Pythagorean Theorem, a%5E2%2Bb%5E2=c%5E2.

Let a=x
Let b=x+4
Let c=20

First, plug in the values for a, b and c, and then simplify.
x%5E2%2B%28x%2B4%29%5E2=20%5E2
x%5E2%2Bx%5E2%2B8x%2B16=400
2x%5E2%2B8x-384=0

From here, solve for x by either factoring, or using the quadratic formula (I'm going to use the quadratic formula).
x+=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x+=%28-%288%29%2B-sqrt%28%288%29%5E2-4%282%29%28-384%29%29%29%2F%282%282%29%29
x=%28-8%2B-sqrt%283136%29%29%2F4
x=%28-8%2Bsqrt%283136%29%29%2F4 or x=%28-8-sqrt%283136%29%29%2F4
x=12 or -16

Now, plug in the values of x into the original formula (x%5E2%2B%28x%2B4%29%5E2=20%5E2})
x%5E2%2B%28x%2B4%29%5E2=20%5E2
12%5E2%2B%2812%2B4%29%5E2=20%5E2
144+256=400
400=400

x%5E2%2B%28x%2B4%29%5E2=20%5E2
%28-16%29%5E2%2B%28%28-16%29%2B4%29%5E2=20%5E2
256+144=400
400=400

By just looking at the numbers, you could conclude that both values of x could be correct. However, we have to look back to our word problem.
The measurement of the telephone pole is x.
Our values of x are 12 and -16.
If we substitute the values of x in,
only x=12 makes sense,
because a telephone pole with height -16 is impossible unless you're measuring from a reference point 16ft above one end of it.