Hard math problem from BB?

Test Preparation SAT Preparation
1

<p>I got this problem wrong about a week ago, and I just did it again but got the same answer. An explanation would be very much appreciated. </p>

<p>This is in the BB 2nd edition, practice test 1, section 3, no. 19.</p>

<p><a href="http://i.imgur.com/8bhRs.jpg%5B/url%5D"&gt;http://i.imgur.com/8bhRs.jpg&lt;/a> (sorry for the crappy photo)</p>

<p>The pyramid shown above has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m?</p>

<p>A. m/sqrt2
B. (m<em>sqrt3)/2
C. m
D. 2m/sqrt3
E. m</em>sqrt2</p>

<p>My reasoning was to look at a cross section, then cut that in half to get a triangle with sides h, m, and m/2. I set X as equal to m/2 to get a 1-2-sqrt3 triangle, so h is equal to x<em>sqrt3. Then I substituted m/2 back in for x, giving (m</em>sqrt3)/2, choice B.</p>

<p>I assume I overcomplicated the problem, but what did I do wrong?</p>

2

<p>Try googling a few words of your question using the search this site:</p>

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/773638-bb2-math-question-page-401-19-a.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/773638-bb2-math-question-page-401-19-a.html&lt;/a&gt;&lt;/p&gt;

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/789767-blue-book-3rd-ed-math-problem-test-1-sec-3-19-help-please.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/789767-blue-book-3rd-ed-math-problem-test-1-sec-3-19-help-please.html&lt;/a&gt;&lt;/p&gt;

<p>You will find the same discussions about problems that are regularly brought here.–(they give pause to many! The beauty is that you will find numerous explanations.</p>

3

<p>Thank you! I didn’t think of searching for the problem; I will do that in the future.</p>

4

<p>Here are two approaches.</p>

<p>First method: Use diagonal of base and two edges to define isosceles triangle. Altitude of that triangle will be same as h.</p>

<p>Second method: recognize face as equilateral triangle; find altitude of that equilateral triangle; use that altitude and m/2 to find h. (This is the method you proposed; check your setup.)</p>

<p>(The “correct” answer would be considered incorrect by many since it has a radical in the denominator.)</p>