SOLUTION: It has been well over 20 years since I have done geometry and trying to assist a friend in high school. The problem is as follows: The longer leg of a right triangle is 6 cm long

Algebra ->  Polygons -> SOLUTION: It has been well over 20 years since I have done geometry and trying to assist a friend in high school. The problem is as follows: The longer leg of a right triangle is 6 cm long      Log On


   

Question 141624: It has been well over 20 years since I have done geometry and trying to assist a friend in high school. The problem is as follows: The longer leg of a right triangle is 6 cm longer than 6 times the shorter leg and 1 cm shorter than the hypoteneuse. Find the perimeter.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
s1=6s2+6
s1=h-1
h-1=6s2+6
h=6s2+6+1
h=6s2+7 now substitute (6s2+7) for h
h^2=s2^2+s1^2
(6s2+7)^2=s2^2+(6s2+7-1)^2
36s2^2+84s2+49=(s2^2+6)^2
36s2^2+84s2+49=s2^2+36s2^2+72s2+36
now cancel out the 36s2^2 terms
s2^2+72s2-84s2+36-49=0
s2^2-12s2-13)=0
(s2-13)(s2+1)=0
s2-13=0
s2=13 for the shorter side.
s1=6*13+6
s1=78+6
s1=84 for the longer side.
84=h-1
h=84+1
h=85 length of the hypotenuse.
proof
85^2=84^1=13^2
7,225=7,056+169
7,225=7,225