SOLUTION: 16. The length of the hypotenuse of a right triangle exceeds the length of the base by 2 cm and exceeds, twice the length of the altitude by 1 cm. Find the length of each side of t

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 16. The length of the hypotenuse of a right triangle exceeds the length of the base by 2 cm and exceeds, twice the length of the altitude by 1 cm. Find the length of each side of t      Log On

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Question 260201: 16. The length of the hypotenuse of a right triangle exceeds the length of the base by 2 cm and exceeds, twice the length of the altitude by 1 cm. Find the length of each side of the triangle.
Answer by edjones(8007) About Me  (Show Source):
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b+2=c
b=c-2
.
2a+1=c
2a=c-1
a=(c-1)/2
.
a^2+b^2=c^2
((c-1)/2)^2+(c-2)^2=c^2
(c^2-2c+1)/4 + c^2-4c+4=c^2
c^2-2c+1+4(c^2-4c+4)=4c^2
c^2-2c+1+4c^2-16c+16=4c^2
c^2-18c+17=0
(c-17)(c-1)=0
c=17
b=15
a=8
.
Ed