Question

Two sides of a triangle measure x cm and 3x cm.
If x is a positive integer which of the following can represent the length of the third side?

Answer 1

Answer:

So the end cases for this question are when x=0 meaning there is only have 1 side and when the sum of the x and 3x sides are the same as 16 as then you would have two straight lines the same length and not a triangle.

So to answer the question given that x is an integer, we start at 1 ( lowest integer that gives us a triangle) and increment up until we are just shy of the maximum.

So,what is the maximum?

The second end case occurs when the two variable sides sum to 16. We can create a formula for this then we can solve it.

x + 3x = 16

or

4x = 16

Thus ( dividing both sides by 4):

x = 4.

So we have x=4 as our second end case that does not result in a triangle.

So how many triangles? There those being for when x=1, x=2 and x=3.

For the curious the sides work out to be:

x=1: 1, 3 and 16

x=2: 2,6 and 16

x=3: 3,9 and 16

Answer 2

Answer:

cases

Explanation:

x is an integer, we start at 1 ( lowest integer that gives us a triangle) and increment up until we are just shy of the maximum ...

the maximum?

The second end case occurs when the two variable sides sum to 16. We can create a formula for this then we can solve it.

x + 3x = 16

or

4x = 16

Thus ( dividing both sides by 4):

x = 4.

therefore we have x=4 as our second end case that does not result in a triangle.

therefore how many triangles? There those being for when x=1, x=2 and x=3.

For the curious the sides work out to be:

x=1: 1, 3 and 16

x=2: 2,6 and 16

x=3: 3,9 and 16

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