Expert: Steve Holleran - 4/3/2008

Question
So I'm taking this practice ACT online, and I got to this triangle question,
which I vaguely remember how to do from Sophomore year, but not really. I
was wondering if you could help? I'd really like to be able to remember how
to do this for the actual test.

Here's the problem as they state it. You should have no problem drawing the
picture of the triangle that's all labeled and stuff that they have.


The manufacturer of an airport baggage conveyer recommends a slope of no
more then 0.25. If the baggage conveyer in the figure below rises 4 feet, what
is the minimum acceptable value for x in feet?

The picture is a right triangle laying down with the ninety degree angle on the
right. the slope rises four feet, and the bottom line is labeled as X.

Thank you so much! =P

Answer
Hi Forrest,

Okay, if the slope can be no more than 0.25, then we need to remember that slope, m, is vertical change / horizontal change.

Some instructors call this m = rise / run.

Here, we have the slope of the conveyer = 4 / x.

Setting this = .25, we have 4 / x <= 0.25

so 4 / 0.25 <= x  -->  16<= x or x >= 16.

So 16 ft is the minimum value.  Any longer x value keeps the slope under .25.

Hope this helps
Steve