Question 1048100: the length of the longer leg, a, of a right triangle is 1 centimeter less than the length of the hypotenuse, and the length of the shorter leg, b, is 8 centimeters less than the length of the hypotenuse. use the pythagorean theorem to write a simplified polynomial equal to c2 using only c as a variable.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the length of the longer leg, a, of a right triangle is 1 centimeter less than the length of the hypotenuse,
and the length of the shorter leg, b, is 8 centimeters less than the length of the hypotenuse.
use the pythagorean theorem to write a simplified polynomial equal to c2 using only c as a variable.
:
a^2 + b^2 = c^2, where
a = c-1
b = c-8
c = the hypotenuse
:
(c-1)^2 + (c-8)^2 = c^2
FOIL
c^2 - 2c + 1 + c^2 - 16c + 64 = c^2
subtract c^2 from both sides
-2c + 1 + c^2 - 16c + 64 = 0
Combine like terms to form a quadratic equation
c^2 - 18c + 65 = 0
Factors to
(c-13)(c-5) = 0
c = 13 is the only reasonable solution
:
:
Check 12^2 + 5^2 = 13^2
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