SOLUTION: The hypotenuse of a right angled triangle is 2 cm. more than its base and 1 cm. more than twice the perpendicular. Find the sides of the triangle?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The hypotenuse of a right angled triangle is 2 cm. more than its base and 1 cm. more than twice the perpendicular. Find the sides of the triangle?      Log On


   

Question 136320: The hypotenuse of a right angled triangle is 2 cm. more than its base and 1 cm. more than twice the perpendicular. Find the sides of the triangle?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = the length of the base. Let the other sides be h and p
h = b+2 ---> b = h-2
h = 2p+1 ---> p = (h-1)/2
we also know h^2 = b^2 + p^2
h%5E2+=+%28h-2%29%5E2+%2B+%28%28h-1%29%2F2%29%5E2+
h%5E2+=+h%5E2+-4h+%2B+4+%2B+%28h%5E2+-2h+%2B+1%29%2F4+
4h%5E2+=+4h%5E2+-+16h+%2B+16+%2B+h%5E2+-2h+%2B1
0+=+h%5E2+-18h+%2B17
0+=+%28h-17%29%28h-1%29
h = 17 or 1.
Since base is h-2, h cannot be one since then b would be negative
so h = 17
b = 15
p = 8