The formulas 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 √hw?

Explanation

Choice C is correct. If Mosteller's and Current's formulas give the same estimate for A, then the right-hand sides of these two equations are equal; that is, √hw / 60 = 4 + w / 30. Multiplying each side of this equation by 60 to isolate the expression √hw gives √hw = 60 (4+w/30) or √hw = 2(4+w). Therefore, if Mosteller's and Current's formulas give the same estimate for A, then √hw is equivalent to 2(4 + w). An alternate approach is to multiply the numerator and denominator of Current's formula by 2, which gives 2(4+w) / /60. Since it is given that Mosteller's and Current's formulas give the same estimate for A, 2(4+w) / 60 = √hw/60.Therefore, √hw = 2(4 + w).