Do not understand this math problem

Test Preparation SAT Preparation
1

<p>If anyone has the official SAT study guide, volume 2, problem 19 on test 1 section 3.</p>

2

<p>Could you please write the problem here?</p>

3

<p>It has a picture that you would need to see in order to understand the problem.</p>

4

<p>Never mind…got it.</p>

<p>Let e and m = 4 (note: e = m);
Draw a line connecting one edge of the square base with the bottom of the altitude;
To find that edge (let’s call it x) you need to use pythagorean theorem on 1/2 of the base;
2^2 + 2^2 = x^2;
x = sqrt(8);
Now, to find h, you can use pythagorean again, keeping in mind that e = 4 and x = sqrt(8);
h^2 + (sqrt(8))^2 = 4^2;
h^2 = 4^2 - sqrt(8)^2;
h^2 = 8;
h = sqrt(8);
h = 2*sqrt(2);</p>

<p>Now, we’re trying to express h in terms of m.
Remember that m = 4;</p>

<p>h = 2*sqrt(2) = 4/sqrt(2);</p>

<p>Therefore, the answer is (A) m/sqrt(2);</p>

5

<p>I’m sorry but I don’t understand your explanation at all. I made a right triangle with the altitude connecting h to a vertices on the square base. Then I know that e=m, and that the diagonal going from the vertices of the square base to the bottom of the altitude h is 1/2 m, because it is 1/2 a diagonal on the square. So I have a 30-60-90 triangle right? Therefore, the altitude h is 1/2m radical 3, but that doesn’t match up with any. I don’t understand why you’re using pythagorean theorem to find that edge that you already know is 1/2 m, or in the case which you put it 1/2 4 which is 2. I don’t think this is a problem that will be well explained over the internet lol, thanks for trying though I appreciate it.</p>

6

<p>Hmm I think you’re going down the wrong path in assuming that it’s a 30-60-90 triangle.
Anyway, it’s a pretty tough problem so I drew a visual.
<a href=“http://i.imgur.com/Z9VWG.jpg[/url]”>http://i.imgur.com/Z9VWG.jpg&lt;/a&gt; Reference it.</p>

<p>The two blue lines are 1/2m;
Let’s have m = 4 again;
We know AC = m = 4;
Let’s find BC.
2^2 + 2^2 = (BC)^2
BC = sqrt(8)
Now that we know BC and AC, we can apply the Pythagorean Theorem to find h.
(sqrt(8))^2 + h^2 = 4^2;
8 + h^2 = 16;
h^2 = 8;
h = sqrt(8);</p>

<p>Now we know h = sqrt (8) AND that m = 4…all that’s left is to find how to express h in terms of m. Easy.
If you enter 4/sqrt(2) into a calculator you’ll find that it equals sqrt(8);
There, 4 = m. Just replace m for 4 and you have m/sqrt(4).</p>

<p>Hopefully that explanation is a bit clearer. If you have any specific questions, I can try to answer them.</p>

7

<p>Ok, now I understand why you did 2^2+2^2 to get BC, but I don’t understand why BC simply also wouldn’t be 2, after all, it’s the same length as the lines draw from the edge of the base to the altitude, at least that’s the way I’m seeing it. Also, I think at the end of your last reply you meant m/sqrt. 2 right?</p>

8

<p>nvm, I understand now that the slant height (BC) would not be the same as the regular height (1/2m) I just would’ve never thought to draw out 2 different triangles, one on the actual base and one with the altitude, vertices, and slant height of the pyramid :&lt;/p>

9

<p>Thanks for your help teteatete, your drawing really helped :)</p>