Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
mark’s garden is a rectangle that is \\(\frac{4a + 96}{a + 15}\\) meters long and \\(\frac{4a + 24}{a + 15}\\) meters wide.
if mark decides to fence his garden, the total length of fencing material required would be \\(\square\\) meters. if he uses prebuilt fence sections that are 50 centimeters wide, he will need \\(\square\\) sections.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). Here, the length \( l=\frac{4a + 96}{a + 15}\) and the width \( w=\frac{4a+24}{a + 15}\).

First, find \( l + w\):

$$
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$$

(We can cancel \( a + 15\) since \( a
eq - 15\) as it would make the denominator zero, and in the context of length and width, \( a\) should be such that the expressions are defined and positive.)

Step2: Calculate the perimeter

Now, use the perimeter formula \( P = 2\times(l + w)\). Since \( l + w=8\), then \( P=2\times8 = 16\) meters. So the total length of fencing material required is 16 meters.

Step3: Calculate the number of fence sections

Each fence section is 50 centimeters wide. First, convert 16 meters to centimeters. Since 1 meter = 100 centimeters, 16 meters \(=16\times100 = 1600\) centimeters.

To find the number of sections, divide the total length (in centimeters) by the width of each section:

$$ \text{Number of sections}=\frac{1600}{50}=32 $$

Answer:

First box: 16; Second box: 32