Question

1. a) write the perimeter of this trapezoid as a polynomial in simplest form.

b) determine the perimeter of the trapezoid when x = 5.
show your work.
trapezoid with sides labeled: top base 5x - 3, bottom base 8x + 2, left and right legs 5x + 6 each

Explanation:

Part (a)

Step 1: Recall the formula for the perimeter of a trapezoid

The perimeter \( P \) of a trapezoid is the sum of the lengths of all its sides. The sides of the trapezoid are \( 5x - 3 \), \( 5x + 6 \), \( 8x + 2 \), and \( 5x + 6 \). So we need to add these expressions together:
\( P=(5x - 3)+(5x + 6)+(8x + 2)+(5x + 6) \)

Step 2: Combine like terms

First, combine the \( x \)-terms: \( 5x+5x + 8x+5x=(5 + 5+8 + 5)x=23x \)
Then, combine the constant terms: \( - 3+6 + 2+6=(-3)+(6 + 2+6)=(-3)+14 = 11 \)
So the perimeter as a polynomial in simplest form is \( P = 23x+11 \)

Part (b)

Step 1: Substitute \( x = 5 \) into the perimeter formula

We found in part (a) that the perimeter \( P=23x + 11 \). Now substitute \( x = 5 \) into this formula:
\( P=23(5)+11 \)

Step 2: Calculate the value

First, calculate \( 23\times5 = 115 \)
Then, add 11: \( 115+11=126 \)

Part (a) Answer:

The perimeter of the trapezoid as a polynomial in simplest form is \( \boldsymbol{23x + 11} \)

Part (b) Answer:

When \( x = 5 \), the perimeter of the trapezoid is \( \boldsymbol{126} \)

Answer:

Step 1: Substitute \( x = 5 \) into the perimeter formula

We found in part (a) that the perimeter \( P=23x + 11 \). Now substitute \( x = 5 \) into this formula:
\( P=23(5)+11 \)

Step 2: Calculate the value

First, calculate \( 23\times5 = 115 \)
Then, add 11: \( 115+11=126 \)

Part (a) Answer:

The perimeter of the trapezoid as a polynomial in simplest form is \( \boldsymbol{23x + 11} \)

Part (b) Answer:

When \( x = 5 \), the perimeter of the trapezoid is \( \boldsymbol{126} \)