Compare Your Answers
Completion requirements
Body surface area (BSA) is a measurement used in the medical field
that approximates the surface area of a human body. The formula is \({\rm{BSA}}
= \sqrt {\frac{{W \cdot H}}{{3\thinspace 600}}} \), where \(W\) is the
weight in kilograms, \(H\) is the height in centimetres, and BSA is measured in square metres.
A newborn baby has an average BSA of \(0.2 \thinspace \rm{m}^2\). Given a baby weighs \(2.7\) kg at birth, what is its height, if the baby has an average BSA? Round to the nearest tenth of a centimetre.
A newborn baby has an average BSA of \(0.2 \thinspace \rm{m}^2\). Given a baby weighs \(2.7\) kg at birth, what is its height, if the baby has an average BSA? Round to the nearest tenth of a centimetre.
Substitute BSA = \(0.2\) m2 and \(W\) = 2.7 kg into the given formula, and solve for \(H\).
\(\begin{align}
{\rm{BSA}} &= \sqrt {\frac{{W\cdot H}}{{3\thinspace 600}}} \\
0.2 &= \sqrt {\frac{{2.7\cdot H}}{{3\thinspace 600}}} \\
\left( {0.2} \right)^2 &= \left( {\sqrt {\frac{{2.7\cdot H}}{{3\thinspace 600}}} } \right)^2 \\
0.04 &= \frac{{2.7\cdot H}}{{3\thinspace 600}} \\
144 &= 2.7\cdot H \\
53.33... &= H \\
53.3 &\doteq H \\
\end{align}\)
The baby is approximately \(53.3\) cm tall.
\(\begin{align}
{\rm{BSA}} &= \sqrt {\frac{{W\cdot H}}{{3\thinspace 600}}} \\
0.2 &= \sqrt {\frac{{2.7\cdot H}}{{3\thinspace 600}}} \\
\left( {0.2} \right)^2 &= \left( {\sqrt {\frac{{2.7\cdot H}}{{3\thinspace 600}}} } \right)^2 \\
0.04 &= \frac{{2.7\cdot H}}{{3\thinspace 600}} \\
144 &= 2.7\cdot H \\
53.33... &= H \\
53.3 &\doteq H \\
\end{align}\)
The baby is approximately \(53.3\) cm tall.
| For further information about solving problems involving radical equations, see p. 299 of Pre-Calculus 11. |