Question

The perimeter of triangle is 22 cm one of its side is 9 cm the difference of the other two side is 7 cm. s=11cm find the area of the triangle

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{a}+\mathrm{b}+\mathrm{c}=22 \\ \mathrm{Let}\mathrm{a}=9 \\ \mathrm{b}-\mathrm{c}=7.....\left(1\right) \\ 9+\mathrm{b}+\mathrm{c}=22 \\ \mathrm{b}+\mathrm{c}=13.....\left(2\right) \\ \mathrm{Adding}\mathrm{equation}1\mathrm{and}2,\mathrm{we}\mathrm{get} \\ 2\mathrm{b}=20 \\ \mathrm{b}=10 \\ \mathrm{So}\mathrm{c}=3 \\ \mathrm{So}\mathrm{area}\mathrm{of}\mathrm{triangle}=\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)} \\ =\sqrt{11\times 2\times 1\times 8} \\ =4\sqrt{11}{\mathrm{cm}}^2 \end{gathered}$$