Question

a monkey sitting at a height of 5 metre on a Tree there is a fruit 10 m from the tree on the ground the monkey gets down as his hungry and goes directly to the fruit if instead he could have climb up to the top of tree and gem directly on the fruit the distance travelled would have been same find height of tree

Answer 1

Hope u like my process
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Let the height of the tree be x m

Now...

If the monkey goes down and went to the fruit, then ,
the distance travelled =10 +5 =15m
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If he climb the tree, distance travelled
=(x-5) m _since he was already 5m top.

While jumping distance travelled
$= \sqrt{ {x}^{2} + {10}^{2} }$
Since then, distance travelled is calcuted through Pythagoras theorem.
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If he climb up on the tree and then jump,
Then the distance travelled
= (x - 5) + (x² + 10²)^½.

Now given that in both cases the distance travelled is same.

So.
$= > (x - 5) + \sqrt{ {x}^{2} + {10}^{2} } = 15 \\ \\ or. \: \: \sqrt{ {x}^{2} + {10}^{2} } = 15 + 5 - x \\ \\ or. \: \: \sqrt{ { x }^{2} + 100 } = (20 - x) \\ \\ or. \: \: {x}^{2} + 100 = {(20 - x)}^{2} \\ \\ or. \: \: {x}^{2} + 100 = {20}^{2} - 2 \times 20 \times x + {x}^{2} \\ \\ or. \: \: {x}^{2} - {x}^{2} + 40x = 400 - 100 \\ \\ or. \: \: 40x = 300 \\ \\ or. \: \: x = \frac{300}{40} = \frac{15}{2} \\ \\ or. \: \: x = 7.5m$
So..
The required height of tree is 7.5 m
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Answer 2

Step-by-step explanation:

Let, AB → Height of tree

BC → Distance of fruit on the ground from tree

M → Position of Monkey on tree

Let,