Question

A triangle has sides $$5\ cm,\ 12\ cm$$ and $$13\ cm$$. Find the length of the perpendicular from the opposite vertex to the side whose length is $$13\ cm$$

Solution

$$AB\perp BC$$$$BD\perp AC$$$$Area(ABC)=\dfrac{1}{2}\times AB\times BC$$ (1)$$Area(ABC)=\dfrac{1}{2}\times BD\times AC$$ (2)Equating (1) and (2)$$\dfrac{1}{2}\times AB\times BC=\dfrac{1}{2}\times BD\times AC$$Let $$AB=12cm,BC=5cm,AC=13cm$$$$AB\times BC= BD\times AC$$ $$12\times 5= BD\times 13$$ $$BD=\dfrac{60}{13}$$$$BD=4.6cm$$The lengh of the perpendicular from the opposite vertex to the side whose length is 13 cm$$=4.6cm$$Maths

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