Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
Solution and Explanation
Let the third side of the triangle be x.
Perimeter of the given triangle = 42 cm
18 cm + 10 cm + x = 42 x
= 14 cm
Perimeter
s =\( \frac{\text{(a + b + c)}}{2}\)
\(= \frac{42}{2} \)
= 21 cm
By Heron’s formula,
Area of a triangle \( = \sqrt{\text{s(s - a)(s - b)(s - c)}}\)
\(= \sqrt{\text{21(21 - 18)(21 - 10)(21 - 14)}}\)
\(= \sqrt{\text{21 × 3 × 11 × 7}}\)
\(= 21\sqrt{11}\) cm2
Area of the triangle \(= 21\sqrt{11}\) cm2.
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