Question

question 8
the diagram below shows the layout of items in a home office. each square in the grid represents one square
foot. the items shown are a desk, chair, bookshelf, file cabinet, and a rug.
if each square in the grid represents a square foot,
which statements are true? choose all that are
correct.
a. the perimeter of the bookshelf is less than 10 ft.
b. the perimeter of the desk is more than 10 feet.
c. the perimeter of the chair is exactly 8 feet.
d. the perimeter of the file cabinet is less than 8 ft.
e. the perimeter of the rug is greater than 14 feet.

Explanation:

Step1: Calculate the perimeter of each item

• Bookshelf: Assume the bookshelf has length \(l = 4\) and width \(w=1\). Using the formula for the perimeter of a rectangle \(P = 2(l + w)\), we get \(P=2(4 + 1)=10\) ft. So statement A is false.
• Desk: Assume the desk has length \(l = 5\) and width \(w = 2\). Using the formula \(P = 2(l + w)\), we get \(P=2(5+2)=14\) ft. So statement B is true.
• Chair: Assume the chair is a square with side \(s = 2\). Using the formula for the perimeter of a square \(P = 4s\), we get \(P = 4\times2=8\) ft. So statement C is true.
• File Cabinet: Assume the file cabinet has length \(l = 3\) and width \(w = 1\). Using the formula \(P=2(l + w)\), we get \(P=2(3 + 1)=8\) ft. So statement D is false.
• Rug: Assume the rug has length \(l = 5\) and width \(w=4\). Using the formula \(P = 2(l + w)\), we get \(P=2(5 + 4)=18\) ft. So statement E is true.

Answer:

B. The perimeter of the desk is more than 10 feet, C. The perimeter of the chair is exactly 8 feet, E. The perimeter of the rug is greater than 14 feet.