Question

The measure of each side of the triangle shown below equals 3x^2+4x+5. Use addition to complete the puzzle using algebraic expressions provided.

Answer 1

To work with the algebraic expression for each side of the triangle, which is given as \(3x^2 + 4x + 5\), we can outline the steps needed to complete a puzzle using addition with this expression.

Assuming you want to find the perimeter of this triangle, which includes the lengths of all three sides, we would add the expression for each side together. Since all three sides are equal in this case, the equation would look something like this:

\[
\text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Side}_3
\]

Since each side is \(3x^2 + 4x + 5\), we can write:

\[
\text{Perimeter} = (3x^2 + 4x + 5) + (3x^2 + 4x + 5) + (3x^2 + 4x + 5)
\]

This simplifies to:

\[
\text{Perimeter} = 3(3x^2 + 4x + 5)
\]

Now, we can distribute the 3:

\[
\text{Perimeter} = 9x^2 + 12x + 15
\]

So, the completed puzzle using addition to find the perimeter of the triangle would yield the resulting expression:

\[
\text{Perimeter} = 9x^2 + 12x + 15
\]

If you meant to have a different operation or a different interpretation of the puzzle, please provide more specific details!