Question

square feet to square inches.)

1. (24) the area of a rectangle is 54 in.². the length of one side of the rectangle is 9 in. find the perimeter of the rectangle.
2. (37) draw a number line and graph the solution of x > 3.
3. (37) write an inequality that describes this graph.

0 1 2 3 4

Explanation:

Problem 5

Step1: Find the width of the rectangle

The area formula of a rectangle is \(A = l\times w\) (where \(A\) is area, \(l\) is length, and \(w\) is width). Given \(A = 54\space in^{2}\) and \(l=9\space in\), we can solve for \(w\) using the formula \(w=\frac{A}{l}\).

$$w=\frac{54}{9}=6\space in$$

Step2: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is \(P = 2(l + w)\). Substitute \(l = 9\space in\) and \(w = 6\space in\) into the formula.

$$P=2(9 + 6)=2\times15 = 30\space in$$

Step1: Draw the number line

Draw a horizontal line. Mark points \(0,1,2,3,4,\cdots\) evenly spaced on it.

Step2: Graph the solution \(x>3\)

Since \(x>3\), we use an open - circle at \(x = 3\) (because \(3\) is not included in the solution set) and draw an arrow to the right of \(3\) to represent all the numbers greater than \(3\).

Step1: Analyze the graph

The graph has a closed - circle at \(x = 2\) (which means \(x = 2\) is included in the solution set) and the arrow is to the right.

Step2: Write the inequality

The inequality that represents the graph is \(x\geq2\)

Answer:

The perimeter of the rectangle is \(30\space in\)

Problem 6