Some doctors base the dosage of a drug to be given to a patient on the patient's body surface area (BSA). The most commonly used formula for calculating BSA is BSA `=sqrt((wh)/(3,600))`, where w is the partient's weight (in kg), h is the patient's height (in cm), and BDA is measured in square meters. How tall (in cm) is a patient who weighs 150kg and has a BSA of `2sqrt(2)m^(2)`?

Answer

To solve the problem, we need to find the height (h) of a patient given their weight (w) and body surface area (BSA) using the formula:

\[ \text{BSA} = \sqrt{\frac{w \cdot h}{3600}} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Weight (w) = 150 kg
- BSA = \( 2\sqrt{2} \) m²

2. **Substitute the known values into the BSA formula**:
\[ 2\sqrt{2} = \sqrt{\frac{150 \cdot h}{3600}} \]

3. **Square both sides to eliminate the square root**:
\[ (2\sqrt{2})^2 = \frac{150 \cdot h}{3600} \]
\[ 8 = \frac{150 \cdot h}{3600} \]

4. **Multiply both sides by 3600 to isolate the term with h**:
\[ 8 \cdot 3600 = 150 \cdot h \]
\[ 28800 = 150 \cdot h \]

5. **Divide both sides by 150 to solve for h**:
\[ h = \frac{28800}{150} \]

6. **Calculate the value of h**:
\[ h = 192 \text{ cm} \]

### Final Answer:
The height of the patient is **192 cm**.

---