Write and simplify an expression to represent the perimeter of the figure. You must show ALL work to earn full credit.

Question

a triangle has 3 sides and both of the sides have 4x-17 the other 3x+9

Answer 1

To find and simplify the expression representing the perimeter of the triangle, we first need to identify the lengths of each of the sides.

The triangle has: Two sides of length \(4x - 17\) and one side of length \(3x + 9\).

Step 1: Write the expression for the perimeter

The perimeter \(P\) of a triangle is the sum of the lengths of all its sides. Therefore, we can express the perimeter as:

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

Substituting the lengths of the sides into the formula, we get:

\[ P = (4x - 17) + (4x - 17) + (3x + 9) \]

Step 2: Combine like terms

Now we can combine the like terms in the expression:

1. First, combine the coefficients of \(x\):

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

2. Next, combine the constant terms:

   \[ -17 - 17 + 9 = -34 + 9 = -25 \]

Putting it all together, we have:

\[ P = 11x - 25 \]

Conclusion

Thus, the simplified expression for the perimeter of the triangle is:

\[ \boxed{11x - 25} \]