SOLUTION: The hypotenuse of a triangle is eight feet longer than the shorter leg. The length of the longer leg is seven feet more than the length of the shorter leg. Find the three sides of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The hypotenuse of a triangle is eight feet longer than the shorter leg. The length of the longer leg is seven feet more than the length of the shorter leg. Find the three sides of       Log On


   

Question 247102: The hypotenuse of a triangle is eight feet longer than the shorter leg. The length of the longer leg is seven feet more than the length of the shorter leg. Find the three sides of the triangle.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
c=a+8
b=a+7
a^2+b^2=c^2
a^2+(a+7)^2=(a+8)^2
a^2+a^2+14a+49=a^2+16a+64
2a^2-a^2+14a-16a+49-64=0
a^2-2a-15=0
(a-5)(a+3)=0
a-5=0
a=5 ans.
b=5+7=12 ans.
c=5+8=13 ans.
Proof:
5^2+12^2=13^2
25+144=169
169=169