The sides of a triangle are 5 cm, 6 cm and 3 cm long. The area of the triangle is $\sqrt{A} c m^{2}$ . Then the value of A is ___.

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Solution

$s = \frac{5 + 6 + 3}{2}$
=7 cm
Area $A = \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{7 (7 - 5) (7 - 6) (7 - 3)}$
$= \sqrt{7 \times 2 \times 1 \times 4}$
$= \sqrt{56} c m^{2}$
The value of A is 56.

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