SOLUTION: Find the lengths of the sides of a triangle if the hypotenuse is 10 centimeters longer than the shorter leg and 5 centimeters longer than the longer leg. i am having a hard time wi

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Question 965851: Find the lengths of the sides of a triangle if the hypotenuse is 10 centimeters longer than the shorter leg and 5 centimeters longer than the longer leg. i am having a hard time with the '5 centimeters longer than the longer leg' part. Thank you in advance.
Shorter leg = x
Hypotenuse = x+10
Longer leg = ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
c=hypotenuse; a=shorter leg=c-10cm; b=longer leg=c-5cm
a%5E2%2Bb%5E2=c%5E2
%28c-10cm%29%5E2%2B%28c-5cm%29%5E2=c%5E2
%28c%5E2-20c%2B100cm%29%2B%28c%5E2-10c%2B25%29=c%5E2 Subtract c^2 from each side.
c%5E2-30C%2B125=0
%28c-5%29%28c-25%29=0
c-5=0 or c-25=0
c=5 or c=25
ANSWER 1: The hypotenuse is 25 centimeters.
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a=c-10cm=25cm-10cm=15 cm
ANSWER 2: The shorter leg is 15 centimeters.
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b=c-5cm=25cm-5cm=20 cm
ANSWER 3: The longer leg is 20 centimeters.
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CHECK:
a%5E2%2Bb%5E2=c%5E2
%2815cm%29%5E2%2B%2820cm%29%5E2=%2825cm%29%5E2
225cm%5E2%2B400cm%5E2=625cm%5E2
625cm%5E2=625cm%5E2