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Hint: Here, we will use the concepts of speed and distance as well as the Pythagorean Theorem i.e.., sum of squares of two adjacent sides of a triangle is equal to the square of the hypotenuse in a right angle triangle.

Given,

A peacock is sitting on the top of a pillar, which is 9 m high, so let us consider â€˜Aâ€™ is the position of peacock and â€˜ABâ€™ be the pillar which is 9 m high. Now, it is also given that from a point 27 m away from the bottom of the pillar a snake is coming to its hole at the base of the pillar. Therefore, let â€˜Câ€™ be the position of the snake at the bottom of the pillar. Therefore, the representation is as follows:

Let Peacock catch the snake at a distance of â€˜xâ€™ m from the bottom of the pillar. So, $AB = 9, BD = x, BC = 27$. Hence the value of â€˜DCâ€™ can be written as

$

\Rightarrow DC = BC - BD \\

\Rightarrow DC = 27 - x \\

$

Now, Using the Pythagorean Theorem, let us find the distance covered by peacock i.e.., AD

$

\Rightarrow A{D^2} = B{C^2} + A{B^2} \\

\Rightarrow A{D^2} = {x^2} + {9^2} \\

\Rightarrow A{D^2} = {x^2} + 81 \\

\Rightarrow AD = \sqrt {{x^2} + 81} \\

$

It is mentioned that the speed of peacock and snake are equal. Therefore, distance covered by the peacock and distance covered by the snake will be equal i.e..,

${\text{Distance covered by peacock(AD) = Distance covered by snake (DC)}}$

$

\Rightarrow AD = DC \\

\Rightarrow \sqrt {{x^2} + 81} = 27 - x \\

$

Squaring on the both sides, we get

$

\Rightarrow {(\sqrt {{x^2} + 81} )^2} = {(27 - x)^2} \\

\Rightarrow {x^2} + 81 = 729 + {x^2} - 54x \\

\Rightarrow 54x = 729 - 81 \\

\Rightarrow 54x = 648 \\

\Rightarrow x = \dfrac{{648}}{{54}} = 12 \\

$

Hence, the snake got caught at a distance of 12m.

Note: As, the speeds of peacock and snake are equal, we have considered distance covered by peacock and snake are equal.

Given,

A peacock is sitting on the top of a pillar, which is 9 m high, so let us consider â€˜Aâ€™ is the position of peacock and â€˜ABâ€™ be the pillar which is 9 m high. Now, it is also given that from a point 27 m away from the bottom of the pillar a snake is coming to its hole at the base of the pillar. Therefore, let â€˜Câ€™ be the position of the snake at the bottom of the pillar. Therefore, the representation is as follows:

Let Peacock catch the snake at a distance of â€˜xâ€™ m from the bottom of the pillar. So, $AB = 9, BD = x, BC = 27$. Hence the value of â€˜DCâ€™ can be written as

$

\Rightarrow DC = BC - BD \\

\Rightarrow DC = 27 - x \\

$

Now, Using the Pythagorean Theorem, let us find the distance covered by peacock i.e.., AD

$

\Rightarrow A{D^2} = B{C^2} + A{B^2} \\

\Rightarrow A{D^2} = {x^2} + {9^2} \\

\Rightarrow A{D^2} = {x^2} + 81 \\

\Rightarrow AD = \sqrt {{x^2} + 81} \\

$

It is mentioned that the speed of peacock and snake are equal. Therefore, distance covered by the peacock and distance covered by the snake will be equal i.e..,

${\text{Distance covered by peacock(AD) = Distance covered by snake (DC)}}$

$

\Rightarrow AD = DC \\

\Rightarrow \sqrt {{x^2} + 81} = 27 - x \\

$

Squaring on the both sides, we get

$

\Rightarrow {(\sqrt {{x^2} + 81} )^2} = {(27 - x)^2} \\

\Rightarrow {x^2} + 81 = 729 + {x^2} - 54x \\

\Rightarrow 54x = 729 - 81 \\

\Rightarrow 54x = 648 \\

\Rightarrow x = \dfrac{{648}}{{54}} = 12 \\

$

Hence, the snake got caught at a distance of 12m.

Note: As, the speeds of peacock and snake are equal, we have considered distance covered by peacock and snake are equal.

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