<p>Here is the question...</p>
<p>What is the greatest possible area of a triangle with one side of length 7 and another side of length 10?</p>
<p>(A) 17
(B) 34
(C) 35
(D) 70
(E) 140</p>
<p>The answer is C, but even after reading the explanations I don't understand.</p>
<p>I thought the Triangle Inequality would apply here, but, I dunno. Help anyone?</p>
<p>a right triangle will have the largest area, but i dunno how to explain that without a lot of trig.</p>
<p>You're making this harder than it actually is....</p>
<p>To find the area of a Triangle, multiply the 2 given sides (7*10), and then divide by 2. The answer is thus 35, and there is no possible way the area can be larger than that.</p>
<p>But how do I know that the third side isn't either the height or base?</p>
<p>if it was the height or base, then it would be smaller than 10, making the triangle smaller.</p>
<p>How do you know the third side would be smaller than 10 though?</p>
<p>The right triangle with sides 7 and 10 will have the BIGGEST possible height of all the triangles possible with sides 7 and 10; therefore, it IS 35.
Draw yourself three triangles.
One right with sides 7 & 10, one obtuse, and one acute..than look at the heights..from there you should be able to understand it.</p>
<p>Sorry but I still don't understand...</p>
<p>Why is it the right triangle with largest area?</p>
<p>ok. here, i drew it. excuse my bad drawing skills. I hope this will make it clear.
<a href="http://i7.tinypic.com/6bnhtz4.jpg%5B/url%5D">http://i7.tinypic.com/6bnhtz4.jpg</a></p>
<p>so the right triangle will always have the greatest area b/c of its height..
Don't read too much into SAT problems, they usually aren't this complicated unless you make them that way. lol XD</p>
<p>LOL thanks akvareli, I loved your drawing. Seriously though, I really appreciate it because this problem is frustrating me. Ok though, so we know that the hypotenuse of the right triangle is not 10, because when the hypotenuse is 10, the area isn't as big as when the height is 10 (and obviously the question is asking for greatest possible)?</p>
<p>if the "hypotenuse" was 10, then the triangle wouldn't be a right triangle if the other sides were 10 and 7.</p>
<p>BTW, there is one more math one I need clarification on (for now at least).</p>
<p>The problem with this problem is, I get what they mean when they list all of the possible ways, but I don't understand their explanation in the 2nd paragraph.</p>
<p>Here is the problem (Pg 14, section 2, #17) <a href="https://satonlinecourse.collegeboard.com/SR/digital_assets/assessment/pdf/0833A611-0A43-10C2-0148-CC8C0087FB06-F.pdf%5B/url%5D">https://satonlinecourse.collegeboard.com/SR/digital_assets/assessment/pdf/0833A611-0A43-10C2-0148-CC8C0087FB06-F.pdf</a></p>
<p>And here is the explanation I don't understand (the 2nd paragraph part)</p>
<p>^ I can't get a hold of the page in the second link. What is the answer btw?</p>
<p>I didn't understand the explanation!
lol</p>
<p>Well, I understand why the answer is 6. You can count up six different pathways.
As for the second paragraph, I understand what the 4! or x! means, but I don't exactly understand the use of it.</p>
<p>Look,I might be a completely stupid by asking this question,but why is 4 in that case?The question asks m-distance,why is 4?</p>
<p>Thanks</p>
<p>b/c four lines is the least amount of lines that you need to get from point F to Z.</p>
<p>Thank you akvareli!</p>
<p>So what is up with the exclamation points?</p>
<p>exclamation point means: like 4!=4<em>3</em>2*1</p>
