Question

assessment practice

1. use the rectangle diagram at the right. 1 8.ar.2.2

part a
write and solve an inequality to find the values of x for which the
perimeter of the rectangle is less than 12.24.
part b
based on your answer to part a, are there any values that can be eliminated
from the solution set? explain.

1. marianna is building a rectangular garden bed. the length is 6\\(\frac{1}{4}\\) feet. she has 20 feet

of boards to make the sides. write and solve an inequality to find the possible width
of her garden bed. 1 8.ar.2.2

Explanation:

Part A

Step1: Write the perimeter formula

The perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l = 4\) and \(w=x\). So \(P=2(4 + x)\)

Step2: Set up the inequality

We want \(P<12.24\), so \(2(4 + x)<12.24\)

Step3: Solve the inequality

Divide both sides by 2: \(4 + x<6.12\)
Subtract 4 from both sides: \(x<6.12 - 4\)
\(x < 2.12\)

Since \(x\) represents a dimension (width) of a rectangle, \(x>0\). So values \(x\leq0\) can be eliminated from the solution set \(x < 2.12\)

Answer:

The inequality is \(2(4 + x)<12.24\) and the solution is \(x < 2.12\)

Part B