Question

mystery message
do each exercise and find your answer at the bottom of the page. write the letter of the exercise in the box above the answer. (assume that figures that appear to be rectangular are rectangles.)
part 1. find the perimeter.
⑤
$3x + 8$ $4x - 1$ $5x + 2$
①
$9x - 10$ $2x^2$ $x^2 + 4$
⑪
$2x - 3$ $4x - 7$
part 2. find the missing side length. the perimeter, $p$, is given.
(s)
$3x - 2$ $6x + 6$ $p = 13x + 11$
(d)
$7x + 2$ $5x$ $4x - 5$ $p = 21x + 2$
(a)
$2x^2 - 9$ $3x + 4$ $p = 3x^2 - 2x - 5$
part 3. find the area.
(e)
$3x$ $8x - 5$
(s)
$2x^2$ $x^2 + 7x + 4$
(q)
$x$ $2x$ $2x$ $x$ $x$
part 4. find the area of the shaded region.
(r)
$9x$ $4x$ $7x - 2$ $16x + 5$
(w)
$6x^2$ $8$ $10x^2 - 3x$ $11x + 20$
(r)
$3x$ $x + 2$ $x + 2$ $x + 2$ $x + 2$ $5x - 12$
$7x^2$ $4x + 7$ $9x^2 - 40x$ $x^2 - 5x$ $116x^2 + 53x$ $12x + 9$ $2x^4 + 9x^3 + 12x^2$ $66x^3 + 40x^2 + 24x$ $24x^2 - 15x$ $12x - 20$ $11x^2 - 44x$ $5x + 5$ $64x^3 + 36x^2 + 30x$ $3x^2 + 9x - 6$ $2x^4 + 14x^3 + 8x^2$
operations with polynomials:
perimeter and area with polynomials
punchline • algebra • book d
©2006 marcy mathworks
12.6

Explanation:

Let's solve one of the problems, say the perimeter of the first triangle (Exercise D) in Part 1.

Step 1: Recall the perimeter formula for a triangle

The perimeter \( P \) of a triangle is the sum of its three sides. So, \( P = \text{side}_1 + \text{side}_2 + \text{side}_3 \).

Step 2: Identify the sides of the triangle

The sides are \( 3x + 8 \), \( 4x - 1 \), and \( 5x + 2 \).

Step 3: Sum the sides

\[

$$\begin{align*} P&=(3x + 8)+(4x - 1)+(5x + 2)\\ &=3x + 8 + 4x - 1 + 5x + 2\\ &=(3x + 4x + 5x)+(8 - 1 + 2)\\ &=12x + 9 \end{align*}$$

\]

Answer:

The perimeter of the triangle (Exercise D) is \( 12x + 9 \).

If you want solutions for other exercises (like the rectangle's perimeter, missing side lengths, areas, or shaded regions), please specify which one, and I'll provide the step - by - step solution.