Question

A rectangle with a width of 30cm has a perimeter from 100cm to 160cm. Graph a compound inequality that shows the possible lengths of the rectangle.
Part A: Use the number line below to graph the solution.
Part B. What type of compound inequality does your solution represent?
The Number line is from 0 to 100 in 10's

Answer 1

100 < perimeter < 160

Perimeter = 2(width + length)
100 < 2(width + length) < 160
50 < 30 + length < 80
20 < length < 50

This inequality shows the possible values of the length

Answer 2

Answer:

Part A) The graph in the attached figure

Part B) $L\geq20\ cm$  and  $L \leq 50\ cm$

Step-by-step explanation:

Part A)

we know that

The perimeter of a rectangle is equal to

$P=2(L+W)$

we have

$W=30\ cm$

and the perimeter

$100\ cm \leq P\leq 160\ cm$

For $P=100\ cm$

$100=2(L+30)$

$L=50-30=20\ cm$

so

$L\geq20\ cm$

For $P=160\ cm$

$160=2(L+30)$

$L=80-30=50\ cm$

so

$L \leq 50\ cm$

The solution of the possible lengths of the rectangle is the interval

$[20,50]$

All real numbers greater than or equal to $20\ cm$ and less than or equal to $50\ cm$

$20\ cm \leq L\leq 50\ cm$

see the graph in the attached figure

Part B)

we know that

A compound inequality contains at least two inequalities that are separated by either "and" or "or". The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities.

In this problem

The compound inequality is equal to

$L\geq20\ cm$  and  $L \leq 50\ cm$