Question

The sides of a triangular plot are 240,100,200 and it's perimeter is 540m. Find it's area.

a) 270√17

b) 900√119

c) 510√7

d) none of these​

Answer 1

option d is the answer mark has brain list

Answer 2

Sides sides of a triangular plot are 240 m, 100 m and 200 m.

Perimeter of plot is 540 m.

We have to find, Area of triangular plot.

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✇ Using Heron's Formula,

$\star\;{\boxed{\sf{\pink{ \sqrt{s(s - a)(s - b)(s - c)}}}}}$

Where,

$\dashrightarrow\sf s = semi - perimeter$

$\dashrightarrow\sf s = \dfrac{Perimeter}{2}$

$\dashrightarrow\sf s = \cancel{ \dfrac{540}{2}}$

$\dashrightarrow\bf s = 270\;m$

Therefore,

$\sf Here \begin{cases} & \sf{a = 240\;m} \\ & \sf{b = 100\;m} \\ & \sf{c = 200\;m} \\ & \sf{s = 270\;m} \end{cases}$

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✇ Now, Putting Values in Formula,

$:\implies\sf \sqrt{270(270 - 240)(270 - 100)(270 - 200)}$

$:\implies\sf \sqrt{270(30)(170)(70)}$

$:\implies\sf \sqrt{270 \times 30 \times 170 \times 70}$

$:\implies\sf \sqrt{96390000}$

$:\implies{\boxed{\frak{\purple{ 900\sqrt{119}\;m^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;Area\;of\;given\; triangle\;is\; \bf{900 \sqrt{119}\;m^2}.}}}$