Question

The length 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.

Answer 1

Here,

$a=5,b=12,c=13$

$s=\frac{1}{2}(a+b+c)=15$

Area of the triangle, A = $\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{15(15-5)(15-12)(15-13)}$

$A=30$ $c{m}^2$

Let p be the length of perpendicular. Then,

$A=\frac{1}{2}\times 13\times p$

Therefore,

$\frac{1}{2}\times 13\times p=30$

$p=\frac{60}{13}$ $cm$