Question 29982: I really need help with this problem. I know it will be a system of equtions but I don't know what those equations would be! Here it is:
A right triangle has a perimeter of 40 units and one leg has a length of 8 units. What are the lengths of the other legs?
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website! Label the three sides as a,b,c, and let a be the hypotenuse.
Suppose a = 8.
Since a is the hypotenuse, then the shortest the other two sides could be is 16 units each, and there is no way that 16² + 16² = 8².
In other words, the side of length 8 cannot be a hypotenuse so it must be one of the other sides.
let c = 8, say.
The perimeter: a + b + c = 40
i.e. a + b = 32
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Pathagoras' theorem: a² = b² + c²
i.e. a² = b² + 64
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Now substitute for a = 32 - b into the quadratic eqn and solve for a.
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