Can some one slove this step by step and explain whats going

Can some one slove this step by step and explain whats going on?

Find the area of a triangle bounded by the x-axis, the line f(x) = 12 - 4x, and the line perpendicular to f that passes through the origin.

Solution

slope of line y =f(x) =12-4x is -4

slope of line perpendicular to f(x)=12-4x is (1_/4) ,since the product of slopes of 2 mutually perpendicular lines is -1

no equation of line with slope (1/4) passing through origin is y =(1_/4)x

so region is bounded by x axis(y=0), y =12-4x, y =(1_/4)x

y =12-4x, y =(1_/4)x

=>12-4x=(1_/4)x

=>48-16x=x

=>17x=48

=>x=48/17

y =(1_/4)x , x=48/17

=> y =(1_/4)(48_/17)=12_/17

height of triangle =12_/17 units

for x intercept of f(x) =12-4x

12-4x=0

=>x=3

base of triangle = 3 units

area of triangle =(1_/2)*base*height

area of triangle =(1_/2)*3*(12_/17)

area of triangle =(18_/17) square units