SOLUTION: The side lengths of a triangle are the integral roots of the equation
x^3 - 16x^2 + 85x - 150 = 0
What is the area of the triangle? (Use Heron's formula for the area of a triangl
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Question 965427: The side lengths of a triangle are the integral roots of the equation
x^3 - 16x^2 + 85x - 150 = 0
What is the area of the triangle? (Use Heron's formula for the area of a triangle)
Answer by amarjeeth123(569) (Show Source): You can put this solution on YOUR website!
By using synthetic division we get x=5 is a root.
x^3 - 16x^2 + 85x - 150 = 0
(x-5)(x^2-11x+30)=0
(x-5)(x^2-5x-6x+30)=0
(x-5)(x(x-5)-6(x-5))=0
(x-5)(x-5)(x-6)=0
The three sides of the triangle are 5,5 and 6.
Semi perimeter s=(5+5+6)/2=16/2=8
Area=√s(s-a)(s-b)(s-c)=√8(8-5)(8-5)(8-6)=√8(3)(3)(2)=√144=12
Answer= 12 square units.
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