Question

The lengths of the side of a triangle are 6cm 8cm and 10cm. Find the length of perpendicular from the opposite vertex to the side whose length is 8cm. By herons formulae.​

Answer 1

$\large\bf\underline{Given:-}$

★ Length of side's of triangle are __

6 cm, 8 cm & 10 cm

$\large\bf\underline {To \: find:-}$

★ Length of perpendicular

$\huge\bf\underline{Solution:-}$

★★ Using Heron's formula , we have to find out the value of S.

$\: \large \bf \: s = \frac{a + b + c}{2}$

$\: \large \bf \: s = \frac{6 + 8 + 10}{2}$

⟹ S = 12

✏Now,

$\bf Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

= √ 12 (12-6) (12-8) ( 12-10)

= √576

=24 cm²

Again,

✏Area of triangle = ½ * Base * Height

⟹ 24 = ½ * 8 * Perpendicular

⟹ Perpendicular = 6 cm

Hence,

the length of perpendicular from opposite vertex to the side whose length is 8 cm is ☞ 6 cm.

${\huge{\mathcal{\tt{Hope \ It \ Helps..!!!}}}}$

Answer 2

answer is 60 do by herons formula