Question 55

What is the area of a triangle whose sides measure 5 cm, 6 cm and 7 cm?

Solution

Given,

Sides of the triangle are 5 cm, 6 cm, 7 cm

Semi perimeter of the triangle (s) = $$\frac{5+6+7}{2}=\frac{18}{2}=9$$

$$\therefore\ $$Area of the triangle = $$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$$

$$=\sqrt{9\left(9-5\right)\left(9-6\right)\left(9-7\right)}$$

$$=\sqrt{9\left(4\right)\left(3\right)\left(2\right)}$$

$$=\sqrt{216}$$

$$=$$ 14.6969 $$cm^2$$

Hence, the correct answer is Option B


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