Mosteller's formula : `A=sqrt(hw)/60`
Current's formula : `A=(4+w)/30`
The formulas above are used in medicine to estimate the body surface area A, in square meters, of infants and children whose weight w ranges between 3 and 30 kilograms and whose height h is measured in Centimeters.
If Mosteller’s and Current’s formulas give the same estimate for A, which of the following expressions is equivalent to `sqrt(hw)` ?

Options

A. `(4+w)/2`
B. `(4+w)/1,800`
C. 2(4 + w)
D. `((4+w)^2)/2`

Explanation

To solve the problem, we need to set the two formulas for body surface area \( A \) equal to each other since they give the same estimate. The formulas are:

1. Mosteller's formula:
\[ A = \frac{\sqrt{hw}}{60} \]

2. Current's formula:
\[ A = \frac{4 + w}{30} \]

Since both formulas give the same estimate for \( A \), we can set them equal to each other:

\[ \frac{\sqrt{hw}}{60} = \frac{4 + w}{30} \]

### Step 1: Cross-multiply to eliminate the fractions.
We can cross-multiply to simplify the equation:

\[ \sqrt{hw} \cdot 30 = (4 + w) \cdot 60 \]

### Step 2: Distribute on the right side.
Now, we distribute \( 60 \) on the right side:

\[ 30\sqrt{hw} = 240 + 60w \]

### Step 3: Isolate \( \sqrt{hw} \).
Next, we divide both sides by \( 30 \) to isolate \( \sqrt{hw} \):

\[ \sqrt{hw} = \frac{240 + 60w}{30} \]

### Step 4: Simplify the right side.
Now, we simplify the right side:

\[ \sqrt{hw} = \frac{240}{30} + \frac{60w}{30} \]
\[ \sqrt{hw} = 8 + 2w \]

### Step 5: Final expression.
Thus, the expression equivalent to \( \sqrt{hw} \) is:

\[ \sqrt{hw} = 2(4 + w) \]

### Conclusion
The final answer is \( 2(4 + w) \).