Hi, there--
PROBLEM:
Find the length of side c of a triangle if side a = 15 and side b = 20.
A SOLUTION:
Is this a right triangle? If yes, then use the Pythagorean Equation 
where
and 
are the lengths of the legs of your triangle, and 
is the length of the
hypotenuse (the longest side.) The hypotenuse is the side across from the right triangle.
Assuming that c is the length of the hypotenuse in your triangle, substitute 15 for a and 20
for b.
Simplify.
We know that c^2 (c times itself) equals 625. We want to know what c is, so we take
the square root of both sides. ( The square root of c^2 is c because c*c=c^2. The square root
of 625 is 25 because 25*25=625.)
The length of c is 25 if the triangle is a right triangle and c is the hypotenuse.
If your triangle is not a right triangle, then there are many correct answers. Use the Triangle
Inequality which states that for any triangle, the sum of the lengths of any two sides must be
greater than the length of the remaining side.
In your triangle, all the following must be true: 15 + 20 > c, and c + 15 > 20, and c + 20 > 15
Solve each inequality:
15 + 20 > c
35 > c
c < 35
c + 15 > 20
c > 20 - 15
c > 5
c + 20 > 15
c > 15 - 20
c > -5
No additional information is gained here. A side length cannot be negative, and we already know from the second inequality that c > 5.
Therefore, 5 < c < 35
The length of c can be any positive number that is greater than 5 and less than 35.
Hope this helps!
Mrs. Figgy
math.in.the.vortex@gmail.com
