SOLUTION: The Hypotenuse of a right triangle is 2cm more than the longer leg, while the longer leg is itself 2cm more than the shorter leg. Find the length of the hypotenuse.
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Question 175282: The Hypotenuse of a right triangle is 2cm more than the longer leg, while the longer leg is itself 2cm more than the shorter leg. Find the length of the hypotenuse. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The Hypotenuse of a right triangle is 2cm more than the longer leg, while the longer leg is itself 2cm more than the shorter leg. Find the length of the hypotenuse.
:
Using a^2 + b^2 = c^2 in this problem:
:
let x = length of the shorter leg (a)
then
(x+2) = length of the longer leg (b)
and
(x+2) + 2 = length of the hypotenuse (c)
which = (x+4)
:
x^2 + (x+2)^2 = (x+4)^2
FOIL
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16
:
Arrange as a quadratic equation on the left:
x^2 + x^2 - x^2 + 4x - 8x + 4 - 16 = 0
x^2 - 4x - 12 = 0
Factor this to
(x-6)(x+2) = 0
The positive solution:
x = 6 cm (the shorter leg)
then
6 + 4 = 10 cm is the hypotenuse
:
:
Check
6^2 + 8^2 = 10^2
36 = 64 = 100
