Question

erin and frannie entered a rug design contest. the rules stated that the rugs dimensions must be 32 inches × 45 inches and that they must be rectangular. they drew the following for their entries. show at least three other designs they could have entered in the contest. calculate the area of each section, and the total area of the rugs. erin 30 2 5 40 frannie 5 30 5 1 30 1

Explanation:

Step1: Find the area of a rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.

Step2: Design 1

Let the rug be divided into three rectangles:

• Rectangle 1: \(l = 10\) inches, \(w=45\) inches. \(A_1=10\times45 = 450\) square inches.
• Rectangle 2: \(l = 10\) inches, \(w = 45\) inches. \(A_2=10\times45=450\) square inches.
• Rectangle 3: \(l = 12\) inches, \(w = 45\) inches. \(A_3=12\times45 = 540\) square inches.

Total area \(A_{total1}=450 + 450+540=1440\) square inches.

Step3: Design 2

Let the rug be divided into three rectangles:

• Rectangle 1: \(l = 32\) inches, \(w = 15\) inches. \(A_1=32\times15=480\) square inches.
• Rectangle 2: \(l = 32\) inches, \(w = 15\) inches. \(A_2=32\times15 = 480\) square inches.
• Rectangle 3: \(l = 32\) inches, \(w = 15\) inches. \(A_3=32\times15=480\) square inches.

Total area \(A_{total2}=480+480 + 480=1440\) square inches.

Step4: Design 3

Let the rug be divided into two rectangles:

• Rectangle 1: \(l = 32\) inches, \(w = 20\) inches. \(A_1=32\times20 = 640\) square inches.
• Rectangle 2: \(l = 32\) inches, \(w = 25\) inches. \(A_2=32\times25=800\) square inches.

Total area \(A_{total3}=640 + 800=1440\) square inches.

Answer:

Design 1: Areas of sections \(450\), \(450\), \(540\) square inches; total area \(1440\) square inches.
Design 2: Areas of sections \(480\), \(480\), \(480\) square inches; total area \(1440\) square inches.
Design 3: Areas of sections \(640\), \(800\) square inches; total area \(1440\) square inches.