The length of sides of a triangle are in the ratio. $17 : 12 : 25$ and its semi perimeter is $270 c m$ . Find the area of the triangle.

9000 c

m^{2}

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6000 c

m^{2}

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7000 c

m^{2}

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8000 c

m^{2}

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Solution

The correct option is A $9000 c$ $m^{2}$
Let the sides of the triangle be $17 x, 12 x$ and $25 x$
Semiperimeter (s) $= \frac{(17 x + 12 x + 25 x)}{2}$
$= 27 x$
Given that,
$27 x = 270 x$
$= 10$
So, the sides of the triangle are $170 c m$ , $120 c m$ and $250 c m$
Semiperimeter $= 270 c m$
Therefore,
Area of the triangle $= \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{270 (270 - 170) (270 - 120) (270 - 250)}$
$= \sqrt{270 (100) (150) (20)}$
$= 9000$ $c m^{2}$

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