SOLUTION: The side of a large tent is in the shape of an isosceled triangle whose area is 54ft^2 and whose base is 6 ft shorter than twice its height. Find the height and the base of the sid

Question 329395: The side of a large tent is in the shape of an isosceled triangle whose area is 54ft^2 and whose base is 6 ft shorter than twice its height. Find the height and the base of the side of the tent.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let height be x
base = 2x-6
Area = 54
..
Area of triangle = 1/2 * base * height
54=1/2 * x*(2x-6)
2*54=x(2x-6)
108=2x^2-6x
2x^2-6x-108=0
divide by 2
x^2-3x-54=0
x^2-9x+6x-54=0
x(x-9)+6(x-9)=0
(x-9)(x+6)=0
x=9 OR x =-6 ignore the negative value
So x=9 feet height
base = 2x-6
base = 2*9-6
base = 18-6
base = 12 feet.
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