SOLUTION: The hypotenuse of a right triangle is 10.2 m long. One leg is 2.1 m shorter than the other leg. Find the lengths of the legs. Round to one decimal place. So I know it's written as

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The hypotenuse of a right triangle is 10.2 m long. One leg is 2.1 m shorter than the other leg. Find the lengths of the legs. Round to one decimal place. So I know it's written as      Log On


   

Question 1059703: The hypotenuse of a right triangle is 10.2 m long. One leg is 2.1 m shorter than the other leg. Find the lengths of the legs. Round to one decimal place.
So I know it's written as (X)^2 + (X-2.1)^2= (10.2)^2
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes now expand the expressions and solve,
X%5E2%2B%28X%5E2-4.2X%2B4.41%29=104.04
2X%5E2-4.2X-99.63=0
Now solve for X using the quadratic formula or completing the square.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(x)^2 + (x-2.1)^2 = (10.2)^2
:
x^2 +x^2 -4.2x +4.41 = 104.04
:
2x^2 -4.2x -99.63 = 0
:
divide both sides of = by 2
:
x^2 -2.1x -49.185 = 0
:
us quadratic formula to solve for x
:
x = ( -(-2.1) + square root( (-2.1)^2 -4*(-49.185) ) ) / (2*1) = 8.1414
x = ( -(-2.1) - square root( (-2.1)^2 -4*(-49.185) ) ) / (2*1) = -6.0414
:
We want the positive value x
:
*******************************************
one leg is 8.1 m and the other leg is 6.0 m
:
(8.1)^2 + (6.0)^2 = (10.2)^2
:
65.61 + 36.0 = 104.04
:
101.61 approx 104.04
:
difference is due to rounding of x value
*******************************************
: