Question 1193656
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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
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<pre>
The line f(x) = 5 - {{{(1/5)x}}}  has x-intercept at  

    5 - {{{(1/5)x}}} = 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 - {{{(1/5)x)}}} = 5x.


Simplifying, we get

    25 - x = 25x

    25 = 25x + x 

    25 = 26x  ---->  x = {{{25/26}}}.


Then y-coordinate of the intercetion point is  y = 5x = {{{5*(25/26)}}} ={{{125/26}}}.


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

by {{{125/26}}}, which is y-coordinate of the intersection point, i.e. its distance from x-axis.


Therefore,  the area of the triangle is  

    area = {{{(1/2)*25*(125/26)}}} = {{{3125/52}}} = 60{{{5/52}}} = 60.096 square units (rounded).    <U>ANSWER</U>
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Solved.