SOLUTION: The hypotenuse of a right triangle is 26cm the sum of the other two sides is 34cm find the lengths of the two sides

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Question 941470: The hypotenuse of a right triangle is 26cm the sum of the other two sides is 34cm find the lengths of the two sides
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the hypotenuse c of a right triangle is 26cm
the sum of the other two sides, a and b, is 34cm
find: the lengths of the two sides
use Pythagoras theorem:
c%5E2=a%5E2%2Bb%5E2
since given the sum a and b and c=26, we have
a%2Bb=34 => a=34-b ...plug in c%5E2=a%5E2%2Bb%5E2

%2826%29%5E2=%2834-b%29%5E2%2Bb%5E2....solve for b
676=1156cm%5E2-68b%2Bb%5E2%2Bb%5E2
676=1156-68b%2B2b%5E2
0=2b%5E2-68b+%2B1156-676
2b%5E2-68b+%2B480=0...divide by 2

b%5E2-34b+%2B240=0
b%5E2-10b-24b+%2B240=0
%28b%5E2-10b%29-%2824b-240%29=0
b%28b-10%29-24%28b-10%29=0
%28b-24%29%28b-10%29=0
solutions:
if %28b-24%29=0=> b=24
if %28b-10%29=0=> b=10
if we choose b=24, then a will be a=34-b=>a=34-24 =>a=10
or if we choose b=10, then a will be a=34-b=>a=34-10 =>a=24
so, it doesn't matter what we choose
a=10 and b=24 is one solution, and
a=24 and b=10 is the other solution