Question

the floor of the school gym is divided into 8 sections. the vertical edges of each section are congruent, and the horizontal edges of each section are congruent. what are the dimensions and area of each section? perimeter = 300 ft

Explanation:

Step1: Set up perimeter equation

The perimeter of the whole gym floor is given by $2(1.5x + x)=300$. Simplifying the left - hand side gives $2(2.5x)=5x$. So, $5x = 300$.

Step2: Solve for x

Dividing both sides of the equation $5x = 300$ by 5, we get $x=\frac{300}{5}=60$ ft.

Step3: Find dimensions of each section

The horizontal edge of each section: The length of the whole floor is $1.5x$ ft and it is divided into 4 equal horizontal - edge sections. So the length of each horizontal edge is $\frac{1.5x}{4}$. Substituting $x = 60$, we have $\frac{1.5\times60}{4}=\frac{90}{4}=22.5$ ft.
The vertical edge of each section: The width of the whole floor is $x$ ft and it is divided into 2 equal vertical - edge sections. So the length of each vertical edge is $\frac{x}{2}$. Substituting $x = 60$, we get $\frac{60}{2}=30$ ft.

Step4: Calculate area of each section

The area of a rectangle is $A = l\times w$. For each section, $l = 22.5$ ft and $w = 30$ ft. So the area of each section is $A=22.5\times30 = 675$ square feet.

Answer:

Each horizontal edge is 22.5 ft, Each vertical edge is 30 ft, The area of each section is 675 square feet.