SOLUTION: Find the area of a triangle bounded by the y axis, the line f(x)=5-1/5x, and the line perpendicular to f(x) that passes through the origin

The line f(x) = 5 -   has x-intercept at  

    5 -  = 0  ---->  25 - x = 0  ---->  x = 25.


So, the hypotenuse of the triangle lies on x-axis and goes from the origin to x= 25,
having the length of 25 units.


The perpendicular line is  y = 5x  (from analysis of slopes).


The intersection point of these two lines  (x-coordinate) can be found as the solution to this equation

    5 -  = 5x.


Simplifying, we get

    25 - x = 25x

    25 = 25x + x 

    25 = 26x  ---->  x = .


Then y-coordinate of the intercetion point is  y = 5x =  =.


Now the area of the triangle is half the product of its hypotenuse, which is 25 units,

by , which is y-coordinate of the intersection point, i.e. its distance from x-axis.


Therefore,  the area of the triangle is  

    area =  =  = 60 = 60.096 square units (rounded).    ANSWER