Question

A triangle has one side that measures 12, another side that measures x, and a third side that measures 4 less than x. The perimeter is 26.

Which equation would we use to find the value of x?

x + x + 4 = 26
x + x - 4 = 26
x + x + 4 + 12 = 26
x + x - 4 + 12 = 26

Answer 1

To find the value of \(x\), we first need to express the sides of the triangle in terms of \(x\):

- One side measures \(x\).
- The second side measures \(12\).
- The third side, which is 4 less than \(x\), can be written as \(x - 4\).

The perimeter of a triangle is the sum of all its sides, and in this case, we know the perimeter is 26. Therefore, we can write the equation for the perimeter as follows:

\[
x + 12 + (x - 4) = 26
\]

Now, simplifying the left side of the equation:

\[
x + 12 + x - 4 = 26
\]
\[
2x + 8 = 26
\]

This matches the structure of the equations given, and we see this can be rearranged to the equivalent form:

\[
x + x - 4 + 12 = 26
\]

Thus, the correct equation to find the value of \(x\) is:

\[
\boxed{x + x - 4 + 12 = 26}
\]