Find the area of a triangle whose sides are respectively $150 c m$ , $120 c m$ , and $200 c m .$

8545.77 sq. cm

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8966.57 sq. cm

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9257.66 sq. cm

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5627.66 sq. cm

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Solution

The correct option is C $8966.57 sq. cm$
Let $a = 150 c m, b = 120 c m$ and $c = 200 c m .$
$s = \frac{a + b + c}{2}$
$\Rightarrow s = \frac{150 + 120 + 200}{2}$
$\Rightarrow s = 235 c m$

Now, by using the heron's formula,
Area $= \sqrt{s (s - a) (s - b) (s - c)}$

$= \sqrt{235 (235 - 150) (235 - 120) (235 - 200)}$

$= \sqrt{235 (85) (115) (35)}$

$= \sqrt{80399375}$

$= 8966.57 sq. cm$

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