Question

a tree is broken at a height of 5cm from the ground and its top touches the ground at distance of 12m from the base of the tree.find the orginal height of the tree​

Answer 1

Given :

• Height at which tree is broken = 5 m
• Top touches the ground at = 12 m

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To Find :

• Original height of tree = ?

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Solution :

~ Formula Used :

• Pythagoras Theorem :

$\large{\color{cyan}{\bigstar}} \; {\underline{\boxed{\orange{\sf{ Hypotenuse² = Height² + Base² }}}}} \; {\color{cyan}{\bigstar}}$

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~ Calculating the Height fell on the ground :

${\dashrightarrow{\qquad{\sf{ Hypotenuse = Height² + Base² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = PQ² + RQ² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = (5)² + (12)² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = 25 + 144 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = 169 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR = \sqrt{169} }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\red{\sf{ Tree \; Fell = 13 \; m }}}}}}}$

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~ Calculating the Original Height :

${\longmapsto{\qquad{\sf{ Original \; Height = Tree{\small_{(Fell)}} + Height{\small_{(Broken)}} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Original \; Height = 13 \; m + 5 \; m }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\color{darkblue}{\sf{ Original \; Height = 18 \; m }}}}}}}$

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~ Therefore :

❛❛ Original Height of the tree is 18 m . ❜❜

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Answer 2

Given :

Height at which tree is broken = 5 m

Top touches the ground at = 12 m

$\\ \rule{200pt}{3pt}$

To Find :

Original height of tree = ?

$\\ \rule{200pt}{3pt}$

Solution :

Formula Used :

Pythagoras Theorem :

$\large{\color{red}{\bigstar}} \; {\underline{\boxed{\red{\sf{ Hypotenuse² = Height² + Base² }}}}} \; {\color{red}{\bigstar}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Calculating the Height fell on the ground :

${\dashrightarrow{\qquad{\sf{ Hypotenuse = Height² + Base² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = PQ² + RQ² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = (5)² + (12)² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = 25 + 144 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR² = 169 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ PR = \sqrt{169} }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\red{\sf{ Tree \; Fell = 13 \; m }}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Calculating the Original Height :

${\longmapsto{\qquad{\sf{ Original \; Height = Tree{\small_{(Fell)}} + Height{\small_{(Broken)}} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Original \; Height = 13 \; m + 5 \; m }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\color{darkblue}{\sf{ Original \; Height = 18 \; m }}}}}}}$

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Therefore :

❛❛ Original Height of the tree is 18 m . ❜❜

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