<p>there are two problems for the practice tests that I am having a lot of trouble understanding. </p>
<ol>
<li>a pyramid has an altitude of h, and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have a length of e. If e = m, what is the value of h in terms of m?</li>
</ol>
<p>a) m/square root of 2
b)m times square root of 3/2
c)m
d)2m/square root of 3
e)m times square root of 2
(srry, didnt know how to do radical symbol!)</p>
<ol>
<li>A salesperson's commission is k percent of the selling price of a car. Which of the following represents the commission in dollars, on 2 cars that sold for $14,000 each?
a)280k
b)7000k
c)28000k
d)14000/(100+2k)
e)(28000 + k)/100</li>
</ol>
<p>OK well first you need to visualize a right triangle inside of the pyramid, we need to first find the bottom length of the triangle. we do this by knowing that the base is a square, and if you were to draw lines connecting the center of the square to the corners it would create a 45-45-90 triangle such that the side lengths must be m/(rad 2). Next we can draw another imaginary triangle, this time using m/(rad 2) and h as side lengths and e as the hypotenuse. we can plug this into the pythagorean theorum, (m/(rad 2))^2 + h^2 = e^2 (m equals e so we can swap those out) (m/(rad 2))^2 + h^2 = m^2. now just solve for h^2 = m^2/2 h=m/(rad 2)</p>