\( 1 \leftarrow \begin{array}{l}\text { A doclor recorded a body-mass index of } 34 \text { on a patient's chart. Later, a nurse notices that the doctor recorded } \\ \text { the patient's weight as } 246 \text { pounds but neglected to record the } \\ \text { patient's height. Find the height. (The formula for body-mass index } \mathrm{B} \text { is given by the equation, } \mathrm{B}=\frac{705 \mathrm{w}}{\mathrm{h}^{2}} \text {, where } \mathrm{w} \text { is } \\ \text { weight in pounds and } \mathrm{h} \text { is height in inches.) } \\ \text { The height of the patient is } \square \text { inches. (Round to the nearest whole number as needed.) }\end{array} \) S...
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To find the height of the patient, we can rearrange the body-mass index (BMI) formula \( B = \frac{705w}{h^2} \) to solve for height \( h \). We know the BMI is 34 and the weight \( w \) is 246 pounds. Plugging in the values, we have: \[ 34 = \frac{705 \times 246}{h^2} \] Now we'll multiply both sides by \( h^2 \): \[ 34h^2 = 705 \times 246 \] Calculating the right side gives us \( 173130 \). Now divide both sides by 34: \[ h^2 = \frac{173130}{34} \approx 5092.65 \] Now, take the square root to find \( h \): \[ h \approx \sqrt{5092.65} \approx 71.4 \] Rounding to the nearest whole number, the height of the patient is approximately \( 71 \) inches. Now, let's add some fun insights! Did you know the concept of BMI was developed in the early 19th century? The formula was created by Belgian mathematician Adolphe Quetelet, who wanted to study the relationship between weight and height among populations. Today, this formula is widely used to assess body weight status and potential health risks—it's pretty fascinating how math can be applied to health! When calculating your own BMI, don’t forget to double-check your numbers. A common mistake is not using the correct units; ensure weight is in pounds and height in inches. Additionally, remember that while BMI is a useful screening tool, it doesn't differentiate between muscle and fat—fit athletes might not always get a fair assessment!
