Question

Using heron's formula find the area of a triangle whose two sides are 9cm and 12 cm and the perimeter is 36

Answer 1

Given=》

a=9cm

b=12cm

c=?

perimeter=36cm

Solution =》

perimeter =a+b+c

36=9+12+c

36=21+c

36-21=c

c=15

Using heron's formula

S=a+b+c/2

s=9+12+15/2

s=36/2

s=18

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

$area = \sqrt{18(18 - 15)(18 - 12)(18 - 9)} \\ area = \sqrt{18 \times 3 \times 6 \times 9} \\ area = \sqrt{6 \times 3 \times 3 \times 6 \times 9} \\ area= 3 \times 6 \sqrt{9} \\ area= 3 \times 6 \times 3 \\ area = 54cm {}^{2}$

Area=54cm²

Answer 2

Answer:

Herons formula

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

perimeter =36

semi perimeter =a+b+c=36

=9+12 +c =36

c= 36_21

c= 15

semi perimeter =

$\frac{36}{2} = 18$

Now using heron formula

$\sqrt{18(18 - 9)(18 - 12)(18 - 15)}$

$= \sqrt{18 \times 9 \times 6 \times 3}$

$= \sqrt{2 \times 3 \times 3 \times 3 \times 3 \times 2 \times 3 \times 3}$

$= 3 \times 3 \times 3 \times 2 = 54$

Hey bro your answer is 54

Hope it is helpful for your