caa5042

Math question

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:

S= a+b+c/ 2

It's a method used to find the third side----know what i'm talkin 'bout?

stupak

are you sure that's the question? Because according to you, we know s, a, and b, so just use 2s - a - b = c.

stupak

you might mean huron's formula for areas = A = sqrt [(S)(s-a)(s-b)(s-c)]

caa5042

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..

how do you use it to find the third side?

stupak

i really don't know unless u knew the area, and the semi perimeter as well as the two sides.

caa5042

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.

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?


I 24
II 20
III 5

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

tripNip

you can find the third side of the triangle using trigonometry, if you have the angle between the known sides

caa5042

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.

snipez90

The "S" in S=a+b+c/2 simply stands for semiperimeter, which makes sense.

Herons is given above but it only useful if you have all three side lengths of a triangle.

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.

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.

goldtx

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.

So, A=0.5x8xh with 0<h<=5

It is easy to see that the area of the triangle cannot be more than 20. So the answer is D.