Question

The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model isBSA =( see picture)where w= weight in kg and h= height in cm. a. Using this model, estimate the height of a person who weighs 76 kg and whose BSA is 1.8. Round your answer to the nearest cm. h=  cm b.  Using this model, estimate the weight of a person who is 164 cm tall and whose BSA is 2.1. Round your answer to the nearest kg. w=  kg 

Answer 1

The given equation of BSA is

$\text{BSA}=\sqrt[]{\frac{wh}{3600}}$

w is the weight in kg

h is the height in cm

a. We need to find the height when

w = 76 kg

BSA = 1.8

Substitute them in the rule above to find h

$1.8=\sqrt[]{\frac{76(h)}{3600}}$

Square both sides to cancel the square root

$\begin{gathered} (1.8)^2=\lbrack\sqrt[]{\frac{76(h)}{3600}}\rbrack^2 \\ 3.24=\frac{76h}{3600} \end{gathered}$

Multiply both sides by 3600

$\begin{gathered} 3.24(3600)=\frac{76h}{3600}(3600) \\ 11664=76h \end{gathered}$

Divide both sides by 76 to find h

$\begin{gathered} \frac{11664}{76}=\frac{76h}{76} \\ 153.4736842=h \end{gathered}$

Round it to the nearest cm

h = 153 cm

b. We need to find the weight when

h = 164 cm

BSA = 2.1

Substitute them in the equation

$2.1=\sqrt[]{\frac{164w}{3600}}$

We will do the same steps above

$\begin{gathered} (2.1)^2=\lbrack\sqrt[]{\frac{164w}{3600}}\rbrack^2 \\ 4.41=\frac{164w}{3600} \end{gathered}$$\begin{gathered} 4.41(3600)=\frac{164w}{3600}(3600) \\ 15876=164w \end{gathered}$$\begin{gathered} \frac{15876}{164}=\frac{164w}{164} \\ 96.80487805=w \end{gathered}$

Round it to the nearest kg

w = 97 kg