SOLUTION: In a right triangle, the lengths of the legs are represented by 7 and r, and the hypotenuse is represented by r + 1. Find the length of the hypotenuse.

Algebra ->  Triangles -> SOLUTION: In a right triangle, the lengths of the legs are represented by 7 and r, and the hypotenuse is represented by r + 1. Find the length of the hypotenuse.      Log On


   

Question 1076331: In a right triangle, the lengths of the legs are represented by 7 and r, and the hypotenuse is represented by r + 1. Find the length of the hypotenuse.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a right triangle, => so, use Pythagorean theorem
c%5E2=a%5E2%2Bb%5E2 where a and b are legs and c hypotenuse

the lengths of the legs are represented by a=7 and b=r, and the hypotenuse is represented by c=r+%2B+1:
c%5E2=a%5E2%2Bb%5E2
%28r+%2B+1%29%5E2=7%5E2%2Br%5E2
r%5E2+%2B2r%2B+1=49%2Br%5E2
cross%28r%5E2%29+%2B2r%2B+1=49%2Bcross%28r%5E2%29
2r=49-1
2r=48
r=48%2F2
r=24
now find hypotenuse:
c=r+%2B+1=> c=24+%2B+1=> highlight%28c=25%29