SOLUTION: The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg.

Question 280586: The hypotenuse of a given right triangle is 6 cm longer than the
shorter leg. The length of the shorter leg is 2 cm less than that of the longer
leg.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a given right triangle is 6 cm longer than the
shorter leg. The length of the shorter leg is 2 cm less than that of the longer
leg.
---
Let shorter leg be "x".
Other leg is "x+2"
Hypotenuse = "x+6"
---------------------
Use Pythagoras to solve for "x" and the length of each side.
(x+6)^2 = x^2 + (x+2)^2
x^2 + 12x + 36 = 2x^2 + 4x+4
x^2 - 8x - 32 = 0
---
Quadratic Formula:
x = [8 +- sqrt(64-4*-32)]/2
---
x = [8 +- sqrt(192)]/2
---
Positive solution:
x = (8 + sqrt(192))/2
x = 10.93 cm (shorter leg)
x+2 = 12.93 cm (other leg)
x+6 = 16.93 cm (hypotenuse)
===============================
Cheers,
Stan H.
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