SOLUTION: Using Quadratic Formula: The hypotenuse of a right triangle is 6 meters long. One leg is 1 meter longer than the other. Find the lengths of both legs of the triangle, to the neare

Algebra ->  Trigonometry-basics -> SOLUTION: Using Quadratic Formula: The hypotenuse of a right triangle is 6 meters long. One leg is 1 meter longer than the other. Find the lengths of both legs of the triangle, to the neare      Log On


   

Question 549665: Using Quadratic Formula:
The hypotenuse of a right triangle is 6 meters long. One leg is 1 meter longer than the other. Find the lengths of both legs of the triangle, to the nearest hindredth of a meter.
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Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
one leg x
the other leg x+1
hypotenuse = 6m
Pythagoras theorem

(Hyp)^2= (leg1)^2+Leg2^2
6^2=x^2+(x+1)^2
36=x^2+x^2+2x+1
36=2x^2+2x+1
2x^2+2x-35=0
Find the roots of the equation by quadratic formula

a= 2 ,b= 2 ,c= -35

b^2-4ac= 4 + 280
b^2-4ac= 284
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%284%29
x1=( -2 + 16.85 )/ 4
x1= 3.71
x2=( -2 -16.85 ) / 4
x2= -4.71