SOLUTION: The hypotenuse of a right triangle is twice as long as the shortest side. The third side is 10√3 cm long. Find the length of the hypotenuse.
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Question 155020: The hypotenuse of a right triangle is twice as long as the shortest side. The third side is 10√3 cm long. Find the length of the hypotenuse.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Let x = shortest side
then from "The hypotenuse of a right triangle is twice as long as the shortest side" we now know:
2x = hypotenuse
.
Additionally, the problem gives us the third side as
.
Finally, pulling it all together AND applying Pythagorean theorem we get:
"(shortest side)^2" + "(third side)^2" = hypothenuse^2
.
We said (from above) that the hypotenuse was 2x
hypotenuse = 2x = = cm
or, in decimal:
hypotenuse = 15.492 cm
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