Question

The perimeter of a triangular park is 11x+1. Two of its three lengths are x + 4 and 3x - 1. What is the missing length?

Answer 1

To find the missing length of the triangular park, we start with the perimeter given by the expression \( 11x + 1 \) and the lengths of two sides, which are \( x + 4 \) and \( 3x - 1 \).

Let's denote the missing length as \( L \). According to the formula for the perimeter of a triangle, the sum of all three sides should equal the perimeter:

\[
(x + 4) + (3x - 1) + L = 11x + 1
\]

Now we can simplify the left side:

First, combine the like terms from \( x + 4 \) and \( 3x - 1 \):

\[
x + 4 + 3x - 1 = 4x + 3
\]

Now we can set up the equation:

\[
4x + 3 + L = 11x + 1
\]

Next, solve for \( L \) by isolating it:

\[
L = 11x + 1 - (4x + 3)
\]

Distributing the negative sign:

\[
L = 11x + 1 - 4x - 3
\]

Now combine like terms:

\[
L = (11x - 4x) + (1 - 3) = 7x - 2
\]

So the missing length \( L \) is:

\[
\boxed{7x - 2}
\]