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.
~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the base length; then the height is 3x units.


Write an equation for the area of the triangle

    {{{(1/2)x*(3x)}}} = 24.


Simplify it and find x

    x*(3x) = 48

    3x^2 = 48

     x^2 = 48/3 = 16

     x = {{{sqrt(16)}}} = 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(4^2 + 12^2)}}} = 16 + {{{sqrt(160)}}} = 16 + {{{4*sqrt(10)}}} = 28.64911 (approximately).
</pre>

Solved in full.