To find the third side of the triangle, you need to use the formula for the perimeter of a triangle, which is the sum of the lengths of the three sides. You can write the formula as:
$$P = a + b + c$$
where $P$ is the perimeter, and $a$, $b$, and $c$ are the sides of the triangle.
You are given that the sides of the triangle are $2x + 1$ and $5x - 3$, and the perimeter is $10x - 12$. You can substitute these values into the formula and solve for the third side, $c$. Here are the steps:
- Step 1: Substitute the values of $P$, $a$, and $b$ into the formula.
$$10x - 12 = (2x + 1) + (5x - 3) + c$$
- Step 2: Simplify the equation by combining like terms.
$$10x - 12 = 7x - 2 + c$$
- Step 3: Isolate $c$ by subtracting $7x - 2$ from both sides.
$$10x - 12 - (7x - 2) = c$$
- Step 4: Simplify the equation by combining like terms.
$$3x - 10 = c$$
- Step 5: Write the final answer.
$$c = 3x - 10$$
Therefore, the answer is:
- The third side of the triangle is $3x - 10$.
If you want to learn more about how to find the sides of a triangle, you can check out these resources:
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