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.

Algebra ->  Triangles -> 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.      Log On


   

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) About Me  (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 +10sqrt%283%29+
.
Finally, pulling it all together AND applying Pythagorean theorem we get:
"(shortest side)^2" + "(third side)^2" = hypothenuse^2
+x%5E2+%2B+%282x%29%5E2+=+%2810sqrt%283%29%29%5E2+
+x%5E2+%2B+4x%5E2+=+100%283%29+
+5x%5E2+=+300+
+x%5E2+=+60+
+x+=+sqrt%2860%29+
+x+=+sqrt%282%2A2%2A15%29+
+x+=+2sqrt%2815%29+
.
We said (from above) that the hypotenuse was 2x
hypotenuse = 2x = +2%282sqrt%2815%29%29+ = +4sqrt%2815%29+ cm
or, in decimal:
hypotenuse = 15.492 cm