SOLUTION: one leg of a right riangle is 1/3m shorter than the other leg. if the hypotenuse of the triangle is 5/3m, find the lengths of both legs.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: one leg of a right riangle is 1/3m shorter than the other leg. if the hypotenuse of the triangle is 5/3m, find the lengths of both legs.      Log On


   

Question 134505: one leg of a right riangle is 1/3m shorter than the other leg. if the hypotenuse of the triangle is 5/3m, find the lengths of both legs.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=b+1/3, c=5/3
a^2+b^2=c^2
(b+ 1/3)^2+b^2=(5/3)^2
b^2+ 2b/3 + 1/9 + b^2 = 25/9
2b^2+ 2b/3 - 24/9 =0
18b^2+6b-24=0 Multiply each side by 9 to eliminate fractions.
6(3b^2+b-4)=0
3*-4=12
what factors of -12=+1 when added? +4, -3 Ans.
3b^2-3b+4b-4=0
3b(b-1)+4(b-1)=0 Factoring by grouping.
(3b+4)(b-1)=0
b=1 m. The only answer for this question.
a=4/3 m.
.
Check:
16/9 + 9/9 =25/9 true
.
Ed