Question

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

• A. $16\sqrt{3}{\text{cm}}^2$
• B. $64{\text{cm}}^2$
• C. $\sqrt{1463}{\text{cm}}^2$
• D. $24\sqrt{3}{\text{cm}}^2$

Answer 1

The correct option is C

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

Third side = perimeter - (sum of other two sides) = 38 - 20 = 18 cm
Semi perimeter of a triangle = $\frac{\text{Perimeter}}{2}=\frac{38}{2}=19\text{cm}$

According to heron's formula,
Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{19(19-12)(19-8)(19-18)}=\sqrt{19\times 7\times 11\times 1}=\sqrt{1463}{\text{cm}}^2$