<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>A RIGHT TRIANGLE with the 2 sides as legs gives the greatest possible area.</p>
<p>So the area is 1/2 bh = 1/2 * 7 * 10 = 35, choice (C).</p>
<p>Advanced explanation: form an “L” with your two hands. Make your right hand the bottom of the L, and your left hand the side of the L. Think of your two hands as the legs of a right triangle - your right hand the base, left the height. Now leave the “base” (rt hand) fixed, while moving your left hand right or left. Notice that either way you go, the height of the corresponding triangle gets smaller (the height is no longer the left hand, but the perpendicular distance from the tips of your fingers to your right hand). Thus, when you fix the base, and another side of a triangle, the right triangle is the one with maximum height, thus maximum area.</p>
<p><a href=“http://talk.collegeconfidential.com/sat-preparation/667622-need-help-math-q.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/667622-need-help-math-q.html</a></p>
<p>I think almost any blue book question has been worked out before – either here at CC or at yahoo answers or somewhere in cyberspace. Google…</p>