The sides of a triangle are in the ratio 5:6:7 and its perimeter is 90 cm. What is the area of this triangle (in square cm)?
\(150\sqrt6\) cm2
Sides in ratio 5:6:7 with perimeter 90 cm give a common factor of \(90\div18=5\), so the sides are 25, 30 and 35 cm.
Semi-perimeter: \(s=45\) cm.
Using Heron's formula: \(\text{Area}=\sqrt{45\times20\times15\times10} = \sqrt{135000}\).
\(\sqrt{135000} = \sqrt{22500\times6} = 150\sqrt6\) cm2.
Hence, the area of the triangle is \(150\sqrt6\) cm2.
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