Question

the length of the side of a triangle are 7 cm 13 cm and 12 cm find the length of perpendicular from the opposite vertex to the side whose length is 12 CM ​

Answer 1

$\huge\mathfrak\purple{Heya\:Mate}$❤

In triangle ABC

AB = 7cm
BC = 13cm
AC = 12cm

s =( 7 + 13 + 12 )/2 = 32/2 = 16cm

$area = \sqrt{s(s - a)(s - b)(s - c)} \\ area = \sqrt{16(16 - 7)(16 - 12)(16 - 13} \\ area = \sqrt{16 \times 9 \times 4 \times 3} \\ area = 4 \times 3 \times 2 \sqrt{3} \\ area = 24 \sqrt{3} c {m}^{2}$

Given :

Base = 12 cm
Height = ?
Area = $24\sqrt{3}$

$area = \frac{1}{2} \times base \times height \\ 24 \sqrt{3} = \frac{1}{2} \times 12 \times height \\ height \: = 24 \sqrt{3} \times \frac{2}{12} \\ height = 4 \sqrt{3} cm$

Hope it helps uhh✌✌✌