SOLUTION: The line y=mx+b forms a triangle with the positive x- & y-axes. If the height is thrice the base, and the area of the triangle is 24 square units, find the equation of the line and

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The line y=mx+b forms a triangle with the positive x- & y-axes. If the height is thrice the base, and the area of the triangle is 24 square units, find the equation of the line and      Log On


   

Question 1167406: The line y=mx+b forms a triangle with the positive x- & y-axes. If the height is thrice the base, and the area of the triangle is 24 square units, find the equation of the line and the perimeter of the triangle.
Answer by ikleyn(52781) About Me  (Show Source):
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The line y=mx+b forms a triangle with the positive x- & y-axes. If the height is thrice the base,
and the area of the triangle is 24 square units, find the equation of the line and the perimeter of the triangle.
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Let x be the base length; then the height is 3x units.


Write an equation for the area of the triangle

    %281%2F2%29x%2A%283x%29 = 24.


Simplify it and find x

    x*(3x) = 48

    3x^2 = 48

     x^2 = 48/3 = 16

     x = sqrt%2816%29 = 4.


Thus the base is 4 units long along x-axis;  the height is 3*4 = 12 units long along y-axis.


It means that the slope is negative 12/4 units, or -3,  and y-intercept is 12 units.


So, we write the equation of the line in the form 

    y = -3x + 12.


The perimeter of the triangle is  4 + 12 + sqrt%284%5E2+%2B+12%5E2%29 = 16 + sqrt%28160%29 = 16 + 4%2Asqrt%2810%29 = 28.64911 (approximately).

Solved in full.