<p>Math question</p>
<p>Guys- i vaguely remember a formula that is usd to find the third side of a triangle when all you're given is two sides(not a 30,60,90 or 45,45,90)... its like:</p>
<p>S= a+b+c/ 2</p>
<p>It's a method used to find the third side----know what i'm talkin 'bout?</p>
<p>are you sure that's the question? Because according to you, we know s, a, and b, so just use 2s - a - b = c.</p>
<p>you might mean huron's formula for areas = A = sqrt [(S)(s-a)(s-b)(s-c)]</p>
<p>thats definitely it...thanks..i remember the sqrt. S(s-a)(s-b)(s-c) part. But i think the first part of the method it to write this out- S= a+b+c/ 2 -I dont know if its necesary though...I always thought there was a franction in there somewhere...anyway..</p>
<p>how do you use it to find the third side?</p>
<p>i really don't know unless u knew the area, and the semi perimeter as well as the two sides.</p>
<p>I wanted to use it to solve this question...I got the answer right but i'm just curious to knwo if that formula can be used.Maybe you can test the trhee areas. </p>
<p>3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?</p>
<p>I 24
II 20
III 5</p>
<p>A. I only
B. II only
C. III only
D. II and III only
E. I, II and III</p>
<p>you can find the third side of the triangle using trigonometry, if you have the angle between the known sides</p>
<p>trip- you dont---i've edited my previous post and included the question. I know its an easy question but i want to see if i can solve it using a definite method rather than using logic.</p>
<p>The "S" in S=a+b+c/2 simply stands for semiperimeter, which makes sense. </p>
<p>Herons is given above but it only useful if you have all three side lengths of a triangle. </p>
<p>That being said, what you could do is use the triangle inequality (two sides of a triangle must be greater than third side) to find the min and max values of the third side, plug each of the two with 5 and 8 (other two sides) into herons, and get an area inequality.</p>
<p>Personally I haven't tried that (similar prob. in red book, used logic), but this type of problem would definitely be one of the last ones on a math section if not the very last, so it MIGHT work. For me, logic is the definite method.</p>
<p>The area of a triangle is 0.5bh (b=base, h=height). With the longer side as the base (i.e., b=8), the height must be greater than zero but less than or equal to 5. </p>
<p>So, A=0.5x8xh with 0<h<=5</p>
<p>It is easy to see that the area of the triangle cannot be more than 20. So the answer is D.</p>