<h1>10 on the official practice SAT from CB</h1>
<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>7o
because triangle 2 sides added together has to be greater than the third side
im guessing</p>
<p>The area of a triangle is 1/2bh. If the height was 10 and the base was 7, the area would be 35. 10 would be the highest possible value for the height, which is why 35 is the correct answer.</p>
<p>I'd say 35. The way I figure that is that you want a right triangle since otherwise either the height or the base is smaller than one of your given sides, and both of those are legs rather than hypotenuse since otherwise your legs (base and height on a right triangle) would be smaller than those, and 1/2 x 7 x 10 = 35.</p>
<p>Google appears to support my assertions.</p>
<p>wait what how can you infer that the height is 10.. maybe i'm thinking something wrong here but can't the third side be anything less than 17? since 10+7 is 17. What page number is this question on?</p>
<p>I don't get any of the above logic... Yes i know two sides of a triangle has to be greater than the third when added up but i don't see how that constitutes to the above explanations. For all you know those two sides could be the legs and the hypotenuse could be anything less than 17.. 16.999999.. so what am i missing? and how do you infer that one of those sides are the height..</p>
<p>yeah i agree with Mde why couldn't the other side be 10? that's what i thought too</p>
<p>the right answer is 35 though..</p>
<p>page number 49 of the sat preparation booklet (same test as the online CB SAT)</p>
<p>the other side can't be 10 because it's askign for the largest value.. what i don't understand is how can you infer 10 is the hight and not just the sides..
diligency what is the page number for the question that it's on?</p>
<p>allright nvmd I'm retarded. So apparently no matter what the value of the third side, if it's greater than 10, it has no effect on the area, but if it's less than 10 then it makes the area smaller. so since it asks for the largest area you treat 7 and 10 as the legs. And the largest area means the largest height and base possible and the largest height possible in a triangle for those measurements is a right triangle since the height is the leg rather than a height in a non-right angle where it's smaller than the leg.. ok did i get that right? lol</p>
<p>First: you can use any side of a triangle as the base. Then the height is the perpendicular distance from the line of that base to the opposite vertex.</p>
<p>Second: say I choose the base to be the side of length 7. Picture that side resting on the ground and the side of length 10 hinged to it at one side. The length of the third side has nothing to do with this. All that matters is how you position the hinge to make the tallest triangle possible so that it will have the max area. That tallest triangle is formed when the hinge makes a right angle.</p>
<p>OR...for those who like to use trig, there is a rule that the area of a triangle is </p>
<p>(1/2) a b sin(theta) where a and b are the lengths of two adjacent sides and theta is the angle between them. The maximum value occurs when theta is 90 degrees.</p>