Question 683957
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 {{{sqrt(15^2+8^2)}}} results: 17