<li>In the figure above (a triagnle not drawn to scale), AC = 6 and BC = 3. Point P (not shown) lies on AB between A and B such that CP is perpendicular to AB. Which of the following could be the length of CP?</li>
</ol>
<p>a. 2
b. 4
c. 5
d. 7
e. 8</p>
<p>PS the figure is not drawn to scale so it does not matter anyway.</p>
<p>Is it a. 2?</p>
<p>it's a. 2</p>
<p>draw the main triangle. then draw the perpendicular line. you'll notice that 3 is the hyp. of one of the triangles, so CP cant be 3, has to be less. only answer that is like that is a</p>
<p>Yea. That was going to be my explanation too.</p>
<pre><code> C
/\
/ | \
6 / | \ 3
/ | \
A /_|\ B
P
</code></pre>
<p>That's a triangle up there. It's meant to be one but it's hard to draw with ASCII.
Well anyway. Angle APC = angle CPB.
That means, in triangle CPA, using Pythagoras' theorem, AC^2=AP^2 + CP^2. (^2 means squared).
Since AC= 6, CP MUST be less than 6.
In triangle CBP, again using Pythagoras' theorem CB^2= CP^2 + PB^2.
And CB=3. So CP MUST be less than 3. The only option that's less than 3 is a. 2. So that's what it must be.</p>
<p>Oh my god. My triangle has been mutilated.</p>