SOLUTION: One leg of a right triangle is 4 m less than the hypotenuse. The other leg is 2 m less than the hypotenuse. Find the length of the hypotenuse.
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Question 204677: One leg of a right triangle is 4 m less than the hypotenuse. The other leg is 2 m less than the hypotenuse. Find the length of the hypotenuse.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let c = the length of the hypotenuse. a and b are the other two legs.
and...
Using the Pythagorean theorem: and making the appropriate substitutions, we get:
Expanding:
Simplifying:
Subtracting from both sides.
Factor the trinomial.
Applying the zero product rule, we have:
or which leads to:
or Discard the second solution as c, the hypotenuse cannot be smaller than either of the other two legs, so...
m is the length of the hypotenuse.
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