Question

The perimeter of this triangular plot of land can be represented by 3x2+10x+20
Enter a polynomial that represents the measure of the third side of the plot of land.

Answer 1

To find the measure of the third side of a triangular plot of land, we first need to know that the perimeter \( P \) of a triangle is the sum of the lengths of all three sides.

Given that the perimeter is represented by the polynomial:
\[
P = 3x^2 + 10x + 20
\]

If we denote the lengths of the first two sides of the triangle as \( a \) and \( b \), the formula for the perimeter can be expressed as:
\[
P = a + b + c
\]
where \( c \) is the length of the third side.

We can rearrange this equation to solve for \( c \):
\[
c = P - (a + b)
\]

Without specific values for \( a \) and \( b \), we can express \( c \) in a general form. If we denote \( a + b \) as a given polynomial, we can represent the third side \( c \).

For example, let's assume:
\[
a + b = k
\]
where \( k \) is a polynomial. Thus, we can say:
\[
c = (3x^2 + 10x + 20) - k
\]

If you have specific values or a polynomial for \( a + b \), you can substitute that into the equation above to find \( c \).

Would you like to specify values for \( a \) and \( b \), or do you want a general form?