SOLUTION: The hypotenuse of a right triangle is 2.6units long. The longer leg is 1.7 longer than the shorter leg. Find the lengths of the sides of the triangle. a) 2.6, 2.5, 0.8 b) 1.0,

Question 184398: The hypotenuse of a right triangle is 2.6units long. The longer leg is 1.7 longer than the shorter leg. Find the lengths of the sides of the triangle.
a) 2.6, 2.5, 0.8
b) 1.0, 2.7, 2.6
c) 2.6, 0.9. 2.6
d) 2.6, 1.7, 4.4
Show work
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
ANSWER A)IS THE CLOSEST.(.78,2.48)
2.6^2=X^2+(X+1.7)^2
6.76=X^2+X^2+3.4X+2.89
2X^2+3.4X+2.89-6.76=0
2X^2+3.4X-3.87=0

X=(-3.4+-SQRT[11.56-4*2*-3.87])/2*2
X=(-3.4+-SQRT[11.56+30.96])/4
X=(-3.4+-SQRT42.52)/4
X=(-3.4+-6.52)/4
X=(-3.4+6.52)/4
X=3.12/4
X=.78 ANS. FOR THE SMALLER SIDE.
.78+1.7=2.48 ANS. FOR THE LONGER SIDE.
PROOF:
2.6^2=.78^2+2.48^2
6.76=.6084+6.1504
6.76=6.76

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