SOLUTION: The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.       Log On


   

Question 113601:
The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
2.4^2=X^2+(X+1.4)^2
5.76=X^2+X^2+2.8X+1.96
2X^2+2.8X+1.96-5.76=0
2X^2+2.8X-3.8=0
2(X^2+1.4X-1.9)=0
USING THE QUADRATIC EQUATION WE GET:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(-1.4+-SQRT[1.4^2-4*1*-1.9])/2*1
X=(-1.4+-SQRT1.96+7.6])/2
X=(-1.4+-SQRT9.56)/2
X=(-1.4+-3.092)/2
X=(-1.4+3.092)/2
X=1.692/2
X=.846 ANSWER FOR THE SHORTER SIDE.
.846+1.4=2.246 ANSWER FOR THE LONGER SIDE.
PROOF
2.4^2=.846^2+2.246^2
5.76=.716+5.044
5.76=5.76