SOLUTION: find the unknown length of the right triangle ; base is x; height is x+2 and the hypotenuse is 10 using the pythagorean theorem

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Question 195288This question is from textbook algebra 1 concepts and skills
: find the unknown length of the right triangle ; base is x; height is x+2 and the hypotenuse is 10 using the pythagorean theorem This question is from textbook algebra 1 concepts and skills

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Pythagorean Theorem,system%28a=base=red%28x%29%2Cb=height=red%28x%2B2%29%2Cc=hypotenuse=red%2810%29%29

a%5E2%2Bb%5E2=c%5E2
x%5E2%2B%28x%2B2%29%5E2=10%5E2
x%5E2%2Bx%5E2%2B4x%2B4-100=0
2x%5E2%2B4x-96=0

*Remember,system%28a=2%2Cb=4%2Cc=-96%29
Solving discriminant, b%5E2-4ac=4%5E2-4%282%29%28-96%29=16%2B768=784

Therefore,
x=%28-4%2B-sqrt%28784%29%29%2F%282%2A2%29=%28-4%2B-28%29%2F4
x=%28-4%2B28%29%2F4=24%2F4=red%286%29, use
x=%28-4-28%29%2F4=-32%2F4=-8, discard (-)


Then,base=6
Also,height=6+2=8

Check, by Pyth theorem:
a%5E2%2Bb%5E2=c%5E2
6%5E2%2B8%5E2=10%5E2
36%2B64=100
100=100


Thank you,
Jojo