Question

If diagonal of a rhombus are in ratio 2:3, and its area is 108cm square. Find the larger diagonal of the rhombus

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{As}\mathrm{diagonals}\mathrm{of}\mathrm{a}\mathrm{rhombus}\mathrm{are}\mathrm{in}\mathrm{ratio}2:3. \\ \mathrm{Let}\mathrm{the}\mathrm{diagonals}\mathrm{be}2\mathrm{a}\mathrm{cm}\mathrm{and}3\mathrm{a}\mathrm{cm}. \\ \mathrm{Now}, \\ \mathrm{Area}\mathrm{of}\mathrm{rhombus}=\frac{1}{2}\times \left(\mathrm{Product}\mathrm{of}\mathrm{its}\mathrm{diagonal}\right) \\ 108=\frac{1}{2}\times \left(2\mathrm{a}\times 3\mathrm{a}\right) \\ 108=3{\mathrm{a}}^2 \\ {\mathrm{a}}^2=36 \\ \mathrm{a}=6\mathrm{cm} \\ 3\mathrm{a}=3\left(6\right)=18\mathrm{cm}\mathrm{ANS}... \end{gathered}$$

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