Question 130770: The flower garden has the shape of a right triangle. 20 ft. of a perennial border forms the hypotenuse of the triangle, and one leg is 4 ft longer than the other leg. Find the lengths of the legs.
I was trying to set up using the pythagorean theorem and for some reason my answers keeps coming up as incorrect.
Setting up the problem as:
Am I doing something wrong?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! looks mighty good to me. Let's see where this takes us:
I'll start by turning things around:
Expand and collect terms:
Put in standard form (
Divide by the lead coefficient to get things in lowest terms:
Finally, factor the trinomial (or complete the square, or use the quadratic formula, according to your preference):
 , because  and 
This says that  or  , but we can exclude the negative root for two reasons. First, because we are looking for a measure of length, a negative number is absurd, and secondly, since in setting up the original equation you squared the variable, you introduced an extraneous root -- one that satisfies the derived equation, but does not satisfy the original problem.
Therefore, the correct answer is that the short leg is 12 feet and the long leg is 16 feet.
Check the answer:
 ,  ,  , and  . Answer checks.
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