Question

to determine proper dosing of a medication, doctors use the formula s = √(wh/3000) to determine a patients body surface area (s in square meters), based on their weight (w, in pounds) and height (h, in centimeters). if someones body surface area is 4 square meters and they are 190 cm tall, how much does the person weigh to the nearest pound? pounds

Explanation:

Step1: Rearrange the formula for body - surface area.

Given $s=\sqrt{\frac{wh}{3000}}$, we square both sides to get $s^{2}=\frac{wh}{3000}$, then $wh = 3000s^{2}$.

Step2: Substitute the known values of $s$ and $h$.

We know $s = 4$ (square meters) and $h=190$ (cm). Substituting into $wh = 3000s^{2}$, we have $w\times190=3000\times4^{2}$.

Step3: Solve for $w$.

First, calculate $3000\times4^{2}=3000\times16 = 48000$. Then $w=\frac{48000}{190}\approx252.63$. Rounding to the nearest pound, $w\approx253$.

Answer:

253