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Question Number 198161 by Blackpanther last updated on 12/Oct/23

Answered by Rasheed.Sindhi last updated on 12/Oct/23

$$▴\mathrm{ABC}=\frac{1}{2}.\mathrm{AC}.\mathrm{BC}$$$$=\frac{1}{2}\times 12\times y=6y$$$$48⩽6y⩽60$$$$8⩽y⩽10$$$$\because y\in \mathbb{Z}$$$$\therefore y=\{8,9,10\}$$$$Now,$$$$\tan \mathrm{A}=\frac{y}{12}=\frac{x}{5}$$$$12x=5y$$$$x=\frac{5y}{12}$$$$\because y=8,9,10$$$$\therefore x=\frac{5\cdot 8}{12},\frac{5\cdot 9}{12},\frac{5\cdot 10}{12}$$$$=\frac{10}{3},\frac{15}{4},\frac{25}{6}$$

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