Question
If a, 12, 16 and b are in continued proportion find a and b.
✓
Answer
$\because a , 12,16, b$ are in continued proportion, then
$
\begin{aligned}
& \frac{a}{12}=\frac{12}{16}=\frac{16}{b} \\
& \Rightarrow \frac{a}{12}=\frac{12}{16} \\
& \Rightarrow 16 a=144 \\
& \Rightarrow a=\frac{144}{16}=9 \\
& \text { and } \frac{12}{16}=\frac{16}{b} \\
& \Rightarrow 12 b=16 \times 16=256 \\
& b=\frac{256}{12}=\frac{64}{3}=21 \frac{1}{3}
\end{aligned}$
Hence $a=9, b=\frac{64}{3}$ or $21 \frac{1}{3}$.
$
\begin{aligned}
& \frac{a}{12}=\frac{12}{16}=\frac{16}{b} \\
& \Rightarrow \frac{a}{12}=\frac{12}{16} \\
& \Rightarrow 16 a=144 \\
& \Rightarrow a=\frac{144}{16}=9 \\
& \text { and } \frac{12}{16}=\frac{16}{b} \\
& \Rightarrow 12 b=16 \times 16=256 \\
& b=\frac{256}{12}=\frac{64}{3}=21 \frac{1}{3}
\end{aligned}$
Hence $a=9, b=\frac{64}{3}$ or $21 \frac{1}{3}$.
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