The-perimeter-of-a-triangle-is-84-cm-and-it-s-area-is-336-square-cm-If-the-length-of-one-side-of-triangle-is-30-cm-then-what-is-the-lengths-of-the-remaining-two-sides-of-triangle-

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Question Number 113080 by bobhans last updated on 11/Sep/20

$$\mathrm{The}\mathrm{perimeter}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{is}$$$$84\mathrm{cm}\mathrm{and}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{area}\mathrm{is}336\mathrm{square}\mathrm{cm}.\mathrm{If}\mathrm{the}$$$$\mathrm{length}\mathrm{of}\mathrm{one}\mathrm{side}\mathrm{of}\mathrm{triangle}\mathrm{is}30\mathrm{cm},\mathrm{then}$$$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{remaining}\mathrm{two}$$$$\mathrm{sides}\mathrm{of}\mathrm{triangle}?$$

Answered by bemath last updated on 11/Sep/20

$$\left(\mathrm{i}\right)\mathrm{perimeter}=84=30+\mathrm{x}+\mathrm{y}$$$$\mathrm{lengths}\mathrm{two}\mathrm{sides}\mathrm{is}\{\begin{array}{l}\mathrm{x}\\ 54-\mathrm{x}\end{array}$$$$\mathrm{then}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{triangle}\mathrm{is}$$$$336=\sqrt{42.(42-30).(42-\mathrm{x}).(42-54+\mathrm{x})}$$$$336=\sqrt{42.12.(42-\mathrm{x}).(\mathrm{x}-12)}$$$$224=(42-\mathrm{x})(\mathrm{x}-12)$$$$224=-504+54\mathrm{x}-{\mathrm{x}}^2$$$${\mathrm{x}}^2-54\mathrm{x}+728=0$$$$\mathrm{x}=\frac{54\pm \sqrt{4}}{2}=\frac{54\pm 2}{2}=27\pm 1$$$$\mathrm{Hence}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{two}\mathrm{sides}\mathrm{of}$$$$\mathrm{triangle}\mathrm{is}\{\begin{array}{l}\mathrm{x}=28,\mathrm{y}=26\mathrm{or}\\ \mathrm{x}=26,\mathrm{y}=28\end{array}$$

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