Find the area of a triangle, two sides of which are 8 cm and 12 cm and the per

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Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm .

Options:

A .

16 \sqrt{3} {cm}^{2}

B .

64 {cm}^{2}

C .

\sqrt{1463} {cm}^{2}

D .

24 \sqrt{3} {cm}^{2}

Answer: Option C
:
C

Third side = perimeter - (sum of other two sides) = 38 - 20 = 18 cm
Semi perimeter of a triangle = $\frac{Perimeter}{2} = \frac{38}{2} = 19 cm$
According to heron's formula,
Area of a triangle $= \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{19 (19 - 12) (19 - 8) (19 - 18)} = \sqrt{19 \times 7 \times 11 \times 1} = \sqrt{1463} {cm}^{2}$

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