Question

Which expression represents the perimeter of the above triangle?
3k + 5
2k + 16
15 + 4k

Answer 1

To represent the perimeter of a triangle, you would typically add together the lengths of all three sides. Given the expressions you provided:

1. \(3k + 5\) (side 1)
2. \(2k + 16\) (side 2)
3. \(15 + 4k\) (side 3)

The perimeter \(P\) of the triangle can be calculated using the formula:

\[
P = \text{side 1} + \text{side 2} + \text{side 3}
\]

Substituting in the expressions for each side, we get:

\[
P = (3k + 5) + (2k + 16) + (15 + 4k)
\]

Now, let's combine all the like terms:

- The \(k\) terms: \(3k + 2k + 4k = 9k\)
- The constant terms: \(5 + 16 + 15 = 36\)

Putting it all together, the expression for the perimeter is:

\[
P = 9k + 36
\]

This is the expression that represents the perimeter of the triangle.