Question

The sides of a triangular plot are in ratio 12:5:10 and it's perimeter is 540m. Find it's area.

a) 270√17

b) 900√119

c) 510√7

d) none of these

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Answer 1

we need to find the sides take the ration in the form of x

perimeter of triangle=540 m

12x+5x+10x=540

27x=540

x=20

sides

12x = 12×20= 240m

5x = 5×20= 100m

10x = 10×20= 200m

The sides are 240m,100m & 200m

Answer 2

Given sides of a triangular plot are in ratio 12:5:10.

Perimeter of triangular plot is 540 m.

We have to find, Area of triangular plot.

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✇ Let the sides of triangular plot be 12x, 5x and 10x.

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

We know that,

✇ Perimeter of triangle = sum of all measure of its all sides

$:\implies\sf 12x + 5x + 10x = 540$

$:\implies\sf 27x = 540$

$:\implies\sf x = \cancel{ \dfrac{540}{27}}$

$:\implies\bf x = 20$

Therefore,

Measure of sides of triangle is,

• 12x = 12 × 20 = 240 m

• 5x = 5 × 20 = 100 m

• 10x = 10 × 20 = 200 m

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✇ Now 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,

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

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

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

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

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

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