Question

If 4 m and 16 are in continued proportion then find the value of m

Answer 1

$\textbf{\underline{Answer :-}}$

The value of m is 8

$\textbf{4 : 8 : : 8 : 16}$

$\textbf{\underline{Explanation :-}}$

Continued Proportion is a Proportion where the mean terms are same.

$\textsf{\underline{Proportion :}}$

4 : m : : m : 16

Mean terms = m and m

Extreme terms = 4 and 16

$\textsf{\underline{According to the rule =}}$

Mean × Mean terms = Extreme × Extreme terms

$\tt{\implies \: m \times m = 4 \times 16}$

$\tt{\implies {m}^{2} = 64 }$

$\tt{\implies \: m = \sqrt{64} }$

To find the value of m we need to find the square root of 64.

$\begin{array}{r|l} 2 & 64 \\\cline{1-2} 2 & 32 \\\cline{1-2} 2 & 16 \\ \cline{1-2} 2 & 8 \\\cline{1-2} 2 & 4\\\cline{1-2}2 & 2 \\\cline{1-2}&1 \end{array}$

64 = 2 × 2 × 2 × 2 × 2 × 2

Make pairs of the Common Factors.

Square root = 2 × 2 × 2 = 4 × 2 = 8

$\tt{\implies \: m = 8}$

Therefore the value of m is 8

$\textbf{\underline{Verification :-}}$

$\tt{\implies8 \times 8 = 16 \times 4}$

$\tt{\implies64 = 64}$

$\therefore$LHS = RHS

$\therefore$The value of m is 8

$\textbf{4 : 8 : : 8 : 16}$