The lengths of two sides of a triangle are 6 and 3. The length of the third side may be

Answer 1

We have a triangle. It is not right triangle, so we need to use triangle inequality to find the length of the third side.

A. The longer side, 6 must be shorter than the sum of the other two sides. If the second side is c, then

6< 3 + c.

The side c must be longer than 3.

B. The side c must be shorter than the sum of the other two sides:

c< 6+3.

Combining A and B we will get that

3 < c < 9.

This interval (3, 9) gives all the lengths the third side of the triangle can have.

Answer 2

You can use the Pythagoream Theorm to find the length of the third side of a triangle given the lengths of the other two sides: a^2 + b^2 = c^2.

a=3

b=6

Substituting the values for a and b, you get:

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2

c = sqrt(45)