Question

The sum of the lengths of any two sides of a triangle much be greater than the third side. If a triangle has a side that is 14cm and a second side that is 1cm less than twice the third side, what are the possible lengths for the second and third side?

How do i work this problem?

Answer 1

The first step is always to make equations out of problems like this.

So let's call the sides x, y, and z. You have:

x = 14
y = 2z - 1
z = ?

So you need to determine which values of y and z could make this true. But, you have one more piece of information: the sume of the lengths of any two sides must be greater than the third side. We have one side that we know and one that we have in terms of another. So we know that:

x + y > z

So:

14 + 2z - 1 > z
2z + 13 > z

Now you can solve to figure out the range of values that z can take, and then you can use that to calculate the range of values that y can take. Does that help?