SOLUTION: A right triangle has 2cm and 9cm respectively less than its hypotenuse. Write an appropriate equation, find the length of each side of the triangle. This is an IB SAMPLE TEST QUEST

Question 683957: A right triangle has 2cm and 9cm respectively less than its hypotenuse. Write an appropriate equation, find the length of each side of the triangle. This is an IB SAMPLE TEST QUESTION.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A right triangle has 2cm and 9cm respectively less than its hypotenuse.
let x = the hypotenuse (c)
then
(x-2) = a
(x-9) = b
:
Write an appropriate equation, find the length of each side of the triangle.
a^2 + b^2 = c^2
therefore:
(x-2)^2 + (x-9)^2 = x^2
FOIL
x^2 - 4x + 4 + x^2 - 18x + 81 = x^2
Combine like terms
x^2 + x^2 - x^2 - 4x - 18x + 4 + 81 = 0
A quadratic equation
x^2 - 22x + 85 = 0
This will factor to
(x-5)(x-17) = 0
only one solution will make sense here
x = 17
:
a: 17 - 2 = 15
b: 17 - 9 = 8
:
the three sides, 8, 15, 17
:
Check this on a calc: enter results: 17
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