math question help plzzz

Test Preparation SAT Preparation
1

<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>since the sum of two sides of a triangle have to be greater than the third, doesn't that mean the third side could be between 4 and 16. so if the third side is 14 then its possible that the area could be 70 (since (14 * 10)/2 = 70). but 140 is impossible.</p>

<p>so i chose D but its C. </p>

<p>I'm guessing your supposed to do just bh/2 with the 7 and 10, the sides they give you but it doesn't say that those have to be the base and height. i think im thinking too much into this cause its supposed to be an easy question. </p>

<p>i think when i thought that the third side could be 14 or whatever, then that 14 and 10 wouldn't have ended up being the base and the height of the triangle so that makes it not work...</p>

<p>i r confuse..</p>

2

<p>You have to know that the hypotenuse does not factor into the area of the triangle, only the two legs do.</p>

<p>In order to assume greatest possible area, assume that 7 and 10 are the lengths of the bases. If they weren’t the legs, and 10 was the hypotenuse then the other leg would be less than 10… and 7 cannot logically be the hypotenuse because we know that the hypotenuse is always the longest side of a triangle.</p>

<p>So the two legs are 7 and 10. 7 * 10 * .5 = 35 (C)</p>