Question

MAX POINTS!

Find the area of a triangle bounded by the y axis, the line f(x)=10-3/4x, and the line perpendicular of f(x) passes through the origin.

Answer 1

`(200)/(3)` square units

Explanation:

Knowing the function and that the triangle is formed by both the x and y-axis, you already have the triangle's height, which is 10 (the y-intercept of the functon) To find the base length, all you have to do is find the x-intercept. To do that, simply:

Set function equal to 0 and solve for x:

f(x) = 10 -
`(3)/(4)` x

0 = 10 -
`(3)/(4)` x

`(3)/(4)` x = 10

x =
`(40)/(3)`

This means that the base length of the triangle is also
`(40)/(3)`. Now that you have the height and base length, you can

Plug values into the formula for the area of a triangle:

The area of a triangle is
`(1)/(2)` × height × base

Height = 10, base =
`(40)/(3)`

Area =
`(1)/(2)` × 10 ×
`(40)/(3)`

Area = 5 ×
`(40)/(3)`

Area =
`(200)/(3)`