Question 245724: The hypotenuse of a right triangle is 25 m long. The length of one leg is 10 m less than twice the other. Find the length of each leg. Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! a^2+b^2=c^2
where c=25 m. and a=2b-10 m.
substitute
(2b-10)^2+b^2=25^2
4b^2-40b+100+b^2=625
5b^2-40b+100=625
divide both sides by 5
b^2-8b+20=125
subtract 20 from both sides
b^2-8b=105
complete the square
take half of 8 and square it=16
add 16 to both sides
b^2-8b+16=121
factor
(b-4)^2=121
and get square root
|b-4|=11
b-4=11
b-4=-11
add 4 to both sides
b=15 and b=-7
