Question

a school gym is divided for a fair by bisecting its width and its length. each half of the length is then bisected, forming 8 sections in all. what are the dimensions and area of each section?
diagram: length 1.5x ft, width x ft, perimeter = 300 ft
each section is □ ft long by □ ft wide. the area of each section is □

Explanation:

Step1: Find the value of \( x \) using the perimeter formula

The perimeter of a rectangle is given by \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width. Here, \( l = 1.5x \) and \( w = x \), and \( P = 300 \) ft.
So, \( 300 = 2(1.5x + x) \)
Simplify inside the parentheses: \( 1.5x + x = 2.5x \)
Then, \( 300 = 2(2.5x) = 5x \)
Solve for \( x \): \( x = \frac{300}{5} = 60 \)

Step2: Determine the length and width of each section

• The width of the gym is \( x = 60 \) ft. It is bisected, so the width of each section is \( \frac{60}{2} = 30 \) ft.
• The length of the gym is \( 1.5x = 1.5\times60 = 90 \) ft. First, it is bisected into two halves: \( \frac{90}{2} = 45 \) ft, then each half is bisected again: \( \frac{45}{2} = 22.5 \) ft. So the length of each section is \( 22.5 \) ft.

Step3: Calculate the area of each section

The area of a rectangle is \( A = l\times w \). Here, \( l = 22.5 \) ft and \( w = 30 \) ft.
So, \( A = 22.5\times30 = 675 \) square feet.

Answer:

Each section is \( 22.5 \) ft long by \( 30 \) ft wide. The area of each section is \( 675 \) square feet.