Question

find the area of triangle side of which are 10 cm and 9 cm and the perimeter 36 CM​

Answer 1

the third side be 'x'

10+9+x = 36

x = 36-19

x = 17

now the total sides are 10, 9, 17.

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

Area of triangle would be

$A \: = \: \sqrt{S(S-A)(S-B)(S-C)}$

$A \: = \: \sqrt{18(18-10)(18-9)(18-17)}$

$A \: = \: \sqrt{18(8)(9)(1)}$

$A \: = \: \sqrt{2×9×2×2×2×9}$

$A \: = \: 2×2×9$

$A \: = \: 36 cm^2$

so the area is

${\huge{\blue{\boxed{36 \:cm^2}}}}$

Answer 2

the first side = 10

the second side= 9

The third side = x

10 + 9 +x = 36

19 + x = 36

x = 36 - 19

x = 17

Now the third side= 17

s = 17 + 10 + 9÷ 2

s= 18

A = √18 (8) (9) (1)

A = √ 2×9×2×2×2×9

A = 2×2×9

A = 36cm square