SOLUTION: Find the hypotenuse of a right triangle with sides 5 inches and 10 inches.

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: Find the hypotenuse of a right triangle with sides 5 inches and 10 inches.      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 169783: Find the hypotenuse of a right triangle with sides 5 inches and 10 inches.
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(31521) About Me  (Show Source):
You can put this solution on YOUR website!
Find the hypotenuse of a right triangle with sides 5 inches and 10 inches.
------------------
c+=+sqrt%285%5E2+%2B+10%5E2%29
= sqrt%28125%29
= 5sqrt%285%29 inches

Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:


Since we can see that the triangle has legs of 5 and 10 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



5%5E2%2B10%5E2=x%5E2 Plug in a=5, b=10, and c=x. Now lets solve for x


2+5+%2B+1+0+0+=++x++%5E+2 Square each individual term



1+2+5+=++x++%5E+2 Combine like terms


s+q+r+t+%28+1+2+5+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


x=5%2Asqrt%285%29 Simplify the square root. Note: only the positive square root is considered

So the answer is x=5%2Asqrt%285%29


Which approximates to x=11.18034


So the hypotenuse is approximately 11.18034 inches