Question

find the area of a triangle of sides 13 cm 14 cm and 15 CM also find the length of a perpendicular from the vertex opposite the side of length 14 cm

Answer 1

Here is your answer...


hope it help you

Answer 2

The length of a perpendicular from the vertex opposite the side of length 14 cm is 12 cm.

Step-by-step explanation:

Given:

Let a = 13 cm, b = 14 cm, c = 15 cm

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

  = $\frac{1}{2}(13+14+15)$

  = $\frac{42}{2}$

  = 21                     [1]

Let A be the area of the given triangle, then

A = $\sqrt{s(s-a)(s-b)(s-c)}$

   = $\sqrt{21(21-13)(21-14)(21-15)}$

   = $\sqrt{21\times8\times7\times6}$

   = $\sqrt{7056}$

A = $84 cm^2$                          [1]

Let p be the length of the perpendicular from vertex D on the side BC, then

A = $\frac{1}{2}\times14\times p$

$2 \times 84 = 14\times p$                  [ from 1 ]

$p = \frac{2\times84}{14}$

p = 12 cm.

Hence the length of a perpendicular from the vertex opposite the side of length 14 cm is 12 cm.