SOLUTION: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altit

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altit      Log On


   

Question 1151121: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altitude of the triangle."
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

base = x
height = x/4
'altitude' is another term for 'height'

Area of triangle = (1/2)*base*height
Area of triangle = (1/2)*x*(x/4)
Area of triangle = (1/2)*x*(1/4)*x
Area of triangle = (1/2)*(1/4)*x*x
Area of triangle = (1/8)*x^2
Area of triangle = 12
(1/8)*x^2 = 12
8*(1/8)*x^2 = 8*12 ... multiply both sides by 8
x^2 = 96
x = sqrt(96) ... note: the base cant be negative
x = sqrt(16*6)
x = sqrt(16)*sqrt(6)
x = 4*sqrt(6) is the base
x/4 = (4*sqrt(6))/4 ... divide both sides by 4
x/4 = sqrt(6) is the altitude