A triangle has sides whose lengths in units are represented by polynomials as shown, where x is a positive integer. Which expression represents the perimeter of the triangle in units?

Answer 1

To find the perimeter of a triangle where the lengths of the sides are represented by polynomials, we need to sum the expressions representing each side of the triangle.

Let’s denote the side lengths of the triangle as follows:

• Side 1: \( a(x) \)
• Side 2: \( b(x) \)
• Side 3: \( c(x) \)

The perimeter \( P \) of the triangle can be calculated using the formula:

\[ P = a(x) + b(x) + c(x) \]

To give you the exact expression, I would need the specific polynomial expressions for \( a(x) \), \( b(x) \), and \( c(x) \). Once you provide those expressions, I can help you simplify that sum to find the perimeter. Please share the expressions for the side lengths.

Answer 2

They are:
3/2x + 5/2
4x +1/4
5x - 3/2

Answer 3

Given the side lengths of the triangle are represented by the following polynomials:

1. \( a(x) = \frac{3}{2}x + \frac{5}{2} \)
2. \( b(x) = 4x + \frac{1}{4} \)
3. \( c(x) = 5x - \frac{3}{2} \)

To find the perimeter \( P \) of the triangle, we need to sum these expressions:

\[ P = a(x) + b(x) + c(x) \]

Substituting in the values:

\[ P = \left( \frac{3}{2}x + \frac{5}{2} \right) + \left( 4x + \frac{1}{4} \right) + \left( 5x - \frac{3}{2} \right) \]

Now, we can combine like terms. First, we add the \( x \) terms:

\[ \frac{3}{2}x + 4x + 5x = \frac{3}{2}x + \frac{8}{2}x + \frac{10}{2}x = \frac{21}{2}x \]

Next, we add the constant terms. We can convert them to a common denominator (which is 4):

• Convert \( \frac{5}{2} \) to quarters: \[ \frac{5}{2} = \frac{10}{4} \]

• \( \frac{1}{4} \) stays the same.

• Convert \( -\frac{3}{2} \) to quarters: \[ -\frac{3}{2} = -\frac{6}{4} \]

Now, we can sum the constants:

\[ \frac{10}{4} + \frac{1}{4} - \frac{6}{4} = \frac{10 + 1 - 6}{4} = \frac{5}{4} \]

Putting it all together, we have:

\[ P = \frac{21}{2}x + \frac{5}{4} \]

Thus, the expression that represents the perimeter of the triangle in units is:

\[ \boxed{\frac{21}{2}x + \frac{5}{4}} \]