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Question

The lengths of the sides of a triangle are $5$ cm, $12$ cm and $13$ cm. Find the length of perpendicular from the opposite vertex to the side whose length is $13$ cm.


A
5013 cm
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B
6013 cm
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C
5916 cm
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D
6019 cm
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Solution


The correct option is B. $\dfrac {60}{13}$ cm

Let's say that the triangle is $ABC$ with $AB = 12, BC = 5, CA = 13$ and $BD \perp AC$

As $AB$ and $BD$ are both perpendiculars( height ) of the $\triangle ABC$ on the bases $BC$ and $AD$, respectively,

$\therefore ar(ABC) = \dfrac{1}{2}  AB \times BC = \dfrac{1}{2} CA \times BD$.

$\Rightarrow BD = \dfrac { AB \times BC } { CA} = \dfrac { 12 \times 5 }{13} = \dfrac {60}{13}$ cm. 

Mathematics

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