Find the area of the triangle, whose sides are 8 cm, 10 cm, and 12 cm long.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(15\sqrt{7}\) cm2
When all three sides of a triangle are known but no height is given, Heron’s formula gives the area: \(\sqrt{s(s-a)(s-b)(s-c)}\), where \(s\) is half the perimeter and \(a\), \(b\), \(c\) are the sides.
Half the perimeter: \(s=\displaystyle\frac{8+10+12}{2}=15\)
The three differences: \(s-a=7\), \(s-b=5\), \(s-c=3\)
Area \(=\sqrt{15\times7\times5\times3}=\sqrt{1575}=\sqrt{225\times7}=15\sqrt{7}\) cm2, taking the perfect square 225 out of the root