SOLUTION: The sum of the squares of the lengths of the three sides of a right triangle is 300 cm2. How many cm are in the length of the hypotenuse? Express you answer in simplest radical for

Algebra ->  Pythagorean-theorem -> SOLUTION: The sum of the squares of the lengths of the three sides of a right triangle is 300 cm2. How many cm are in the length of the hypotenuse? Express you answer in simplest radical for      Log On


   

Question 238960: The sum of the squares of the lengths of the three sides of a right triangle is 300 cm2. How many cm are in the length of the hypotenuse? Express you answer in simplest radical form.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can start with the Pythagorean theorem:
1) c%5E2+=+a%5E2%2Bb%5E2 and ...
2) a%5E2%2Bb%5E2%2Bc%5E2+=+300 "The sum of the squares of the lengths of the three sides of a right triangle is 300 sq.cm."
Solve equation 2) for c%5E2
2a) c%5E2+=+300-%28a%5E2%2Bb%5E2%29 Substitute a%5E2%2Bb%5E2+=+c%5E2
2b) c%5E2+=+300-c%5E2 Add c%5E2 to both sides.
2c) 2c%5E2+=+300 Divide both sides by 2.
2d) c%5E2+=+150 Take the square root of both sides.
2e) c+=+sqrt%28150%29 Simplify, noting that sqrt%28150%29+=+sqrt%2825%2A6%29.
2f) highlight%28c+=+5%2Asqrt%286%29%29cm.
The length of the hypotenuse is 5%2Asqrt%286%29cm.