Question

The body surface area A of a human being is used to determine approximate doses of medication using the formula A = sqrt((wh)/3131), where w is the weight (lb) and h is the height (in.). If A must be less than 1.8 for a person that weighs 170 lb, how many inches tall can a patient be for the dose to be appropriate?

A) 80 inches
B) 60 inches
C) 70 inches
D) 90 inches

Answer 1

Using the formula A = sqrt((wh)/3131), for a patient weighing 170 lb to have a BSA less than 1.8, they can be approximately 60 inches tall, which is option B.

Step-by-step explanation:

The question asks for the maximum height a patient can be for their body surface area (BSA) to be less than 1.8, given they weigh 170 lb. Using the provided formula A = sqrt((wh)/3131) and solving for h, we get the following steps:

1. Plug in the known values A = 1.8 and w = 170 lb into the formula: 1.8 = sqrt((170*h)/3131).
2. Square both sides to eliminate the square root: 3.24 = (170*h)/3131.
3. Multiply both sides by 3131 to isolate 170h: 10144.84 = 170h.
4. Divide by 170 to solve for h: h ≈ 59.68 inches.

Given the options A) 80 inches, B) 60 inches, C) 70 inches, D) 90 inches, the patient can be 60 inches tall (option B) for the dose to be appropriate, as 59.68 rounds up to 60.