SOLUTION: Find the length x in each triangle. Express your answer in simplified radical form. Side 1: 10 Side 2: 8 Bottom: x I need some help with this problem. Thanks

Algebra ->  Radicals -> SOLUTION: Find the length x in each triangle. Express your answer in simplified radical form. Side 1: 10 Side 2: 8 Bottom: x I need some help with this problem. Thanks      Log On


   

Question 74137: Find the length x in each triangle. Express your answer in simplified radical form.
Side 1: 10 Side 2: 8 Bottom: x
I need some help with this problem. Thanks
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to guess that the triangle you were given is a right triangle (one of the angles is
90 degrees and the two shortest sides meet to form that 90 degree angle). The longest
side is called the hypotenuse and it is likely to be side 1 (length 10) in the problem.
.
If this is the case, then we can use a rule called the Pythagorean theorem which says that
"the sum of the squares of the two legs (short sides) of a right triangle are equal to
the square of the hypotenuse (longest side). In equation form this would be:
.
a%5E2+%2B+b%5E2+=+c%5E2
.
Now all we have to do is substitute your given values into this equation. c is the long
side and, as I view your problem, is 10. So substitute 10 for c and the equation becomes:
.
a%5E2+%2B+b%5E2+=+10%5E2
.
One of the short sides is known to be 8. It doesn't matter whether we call it b or a. Either
one will work. So lets call it b as long as there's no difference.
.
Substitute 8 for b and the equation becomes:
.
a%5E2+%2B+8%5E2+=+10%5E2
.
Then let's substitute x for "a" so that the unknown side matches what the problem calls it.
.
We know that 8%5E2+=+64 and 10%5E2+=+100 so let's substitute those two values to
get:
.
x%5E2+%2B+64+=+100
.
Then eliminate the 64 on the left side by subtracting 64 from both sides. When you do that
the equation reduces to:
.
x%5E2+=+36
.
You can solve this equation for “a” by taking the square root of both sides to get:
.
sqrt%28x%5E2%29+=+sqrt%2836%29
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And this simplifies to:
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x+=+6
.
That’s the answer for this triangle. The side you are missing has to be the shortest side
and it is 6 units long.
.
I hope that I was right in guessing that you were dealing with a right triangle. If it's not
the case, then I apologize, and you'll have to post again with more information about the
triangle so that a tutor can understand what the triangle looks like.
.
In either case, I hope that you gain an understanding of the use of the Pythagorean theorem.
The Pythagorean theorem ONLY works on RIGHT triangles so don’t try to use it on just any
old triangle that comes along.