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Body mass index (BMI) is one measure of obesity.

BMI is calculated using the equation:
[tex]\[ \text{BMI} = \frac{\text{body mass in } kg}{(\text{height in } m)^2} \][/tex]

Table 1 shows how BMI is used to describe an adult's BMI category.

Table 1

\begin{tabular}{|l|c|}
\hline
BMI & BMI category \\
\hline
[tex]$\ \textless \ 18.5$[/tex] & Underweight \\
\hline
18.5 to 24.9 & Healthy weight \\
\hline
25.0 to 29.9 & Overweight \\
\hline
[tex]$\ \textgreater \ 29.9$[/tex] & Obese \\
\hline
\end{tabular}

A person is [tex]\(1.64 \, m\)[/tex] tall and has a mass of [tex]\(69 \, kg\)[/tex].

Determine the BMI category for this person. Use the BMI equation and Table 1.

Sagot :

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To determine the BMI category for a person who is 1.64 meters tall and has a mass of 69 kilograms, we first need to calculate the BMI using the given formula:

[tex]\[ \text{BMI} = \frac{\text{body mass in kg}}{(\text{height in m})^2} \][/tex]

Let's break this calculation down step-by-step:

1. Identify the given variables:
- Body mass (weight) = 69 kg
- Height = 1.64 m

2. Substitute the given values into the BMI formula:

[tex]\[ \text{BMI} = \frac{69}{(1.64)^2} \][/tex]

3. Calculate the height squared:

[tex]\[ (1.64)^2 = 2.6896 \][/tex]

4. Divide the body mass by the squared height:

[tex]\[ \text{BMI} = \frac{69}{2.6896} \approx 25.654 \][/tex]

So, the calculated BMI for this person is approximately 25.654.

Next, we use Table 1 to categorize this BMI value:

- Underweight: BMI < 18.5
- Healthy weight: BMI 18.5 to 24.9
- Overweight: BMI 25.0 to 29.9
- Obese: BMI > 29.9

Given that the calculated BMI is 25.654, we see that it falls within the range of 25.0 to 29.9. Therefore, according to Table 1:

- The BMI category is Overweight.

So, the person's BMI category is Overweight.
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