The perimeter of a triangle, two of whose sides are 18 cm and 10 cm is 42 cm. Find the area of the triangle.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(21\sqrt{11}\) cm2
The perimeter gives the third side, and with all three sides known the area comes from Heron’s formula, \(\sqrt{s(s-a)(s-b)(s-c)}\), where s is half the perimeter.
Third side: \(42-18-10=14\) cm
\(s=\frac{42}{2}=21\); \(s-a=3\), \(s-b=11\), \(s-c=7\)
Area \(=\sqrt{21\times3\times11\times7}=\sqrt{441\times11}=21\sqrt{11}\) cm2