Question 423229: one leg of a right triangle is twice as long as the other leg. the length of the hypotenuse is 20 squared. what is the length of each leg
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Assume the legs are a, b, and c.
c = the hypotenuse.
c = 20^2
c = 400
.
One leg is twice as long as the other.
a = 2b
.
The Pythagorean Theorem teaches us:
c^2 = a^2 + b^2
.
Substituting what we know...
400^2 = (2b)^2 + b^2
160000 = 4b^2 + b^2
160000 = 5b^2
Divide both side by 5.
32000 = b^2
Take the square root of both sides.
sqrt(32000) = b
.
sqrt(32 000) = 178.885438
so
b = 178.885438
.
Looking back, we see that
a = 2b
so
a = 2 * 178.885438
a = 357.770876
.
Always check your answer.
In this case you do so by checking to see if c^2 = a^2 + b^2.
Is this equation true?
a^2 = 128,000
b^2 = 32,000
a^2 + b^2 = 160,000
That checks.
.
Remember to state the answer clearly.
The legs of the right triangle are 178.885438 and 357.770876.
.
Done.
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