Question

$\huge\bold\purple{QueStion}$
find area of triangle if its perimeter is 32 cm if its length of 2 sides is 8 cm and 12 cm respectively​

Answer 1

★ side a + side b + side c = 32

★ 8 + 12+ side c = 32

★ 20 + side c = 32

★ side c = 32 - 20

★ side c = 12

Answer 2

Perimeter of the Triangle = 32 cm

Length of two sides of triangle = 8 cm, 12cm

Therefore, the third side = 32 - (8 + 12) cm

= 32 - 20 cm

= 12 cm

Let a = 8 cm, b = 12 cm, c = 12 cm

According to Heron's Formula,

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

$=> s = \frac{8 + 12 + 12}{2} \: \: cm$

$=> s = \frac{32}{2} \: cm$

$= > s = 16 cm$

Now, Area of the Triangle =

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

$= \sqrt{16 \times (16 - 8) \times (16 - 12) \times (16 - 12)}$

$= \sqrt{16 \times 8 \times 4 \times 4}$

$= \sqrt{2048}$

$= 45.25 \: cm^{2} \: \: \: approx.$