SOLUTION: The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the legnths of the legs of the triangle.

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a2 + b2 = c2 is the formula for Pythagorean Theorem
a2 = 14
b = b unsolved
c2= 26
14(2) + b = 26(2)
196 + b(2) = 676
Subtract 196 from 676
b= 480
b= square 21.90

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Let a = shorter leg
Let b = longer leg
let c = hypoteneuse
a is 14 feet shorter than b:
a+14=b

we can substitute a+14 in for our b, and use the hypoteneuse value of 26:



divide both sides by two:

subtract 338 from both sides:


a=-24 or a=10
we can rule out the -24, because we are talking about a distance, which is always positive:
so the shorter leg = 10 feet
Put this back into the equation:
a+14=b
10+14=24, so the longer leg is 24 feet
and this makes sense because
10^2 + 24^2= 100 +576 = 676
and 26*26 = 676