Question

Q). The height of a tree varies as the square root of its age (between 5 and 17 years). When the age of a tree is 9 years, its height is 4 feet. What will be the height of the tree at the age of 16 (in inches)?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{us}\mathrm{assume}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{tree}\mathrm{is}\mathrm{H}\mathrm{and}\mathrm{its}\mathrm{age}\mathrm{is}\mathrm{A}\mathrm{years} \\ \mathrm{So},\mathrm{H}\mathrm{is}\mathrm{directly}\mathrm{proportional}\mathrm{to}\sqrt{\mathrm{A}} \\ \mathrm{or}\mathrm{H}=\mathrm{K}\sqrt{\mathrm{A}} \\ \mathrm{Now},4=\mathrm{k}\sqrt{9}\left(\mathrm{as}\mathrm{A}=9\right) \\ \Rightarrow 4=3\mathrm{K} \\ \Rightarrow \mathrm{K}=\frac{4}{3} \\ \mathrm{So},\mathrm{height}\mathrm{at}\mathrm{the}\mathrm{age}\mathrm{of}16\mathrm{yrs}=\mathrm{H}=\mathrm{K}\sqrt{\mathrm{A}} \\ =\frac{4}{3}\times \sqrt{16} \\ =\frac{16}{3} \\ =5\mathrm{feet}4\mathrm{inhes}. \\ =\left(5\times 12\right)\mathrm{inches}+4\mathrm{inches} \\ =64\mathrm{inches}\left(1\mathrm{feet}=12\mathrm{inches}\right) \end{gathered}$$
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