Question

A tree is broken at a height of 5 m from the ground and its top touches the ground at a

distance of 12 m from the base of the tree. Find the original height of the tree.​

Answer 1

Given :

• A tree is broken at a height of 5 m from the ground.
• The top of the tree touches the ground at a distance of 12 m from the base of the tree.

To find :

• The original height of the tree

Concept :

The height of the tree which is broken from the ground will be the perpendicular and the top of the tree which touches the ground at a distance of 12 m from the base of the tree will be the base of the right - angled triangle. So, firstly calculate the hypotenuse using pythagoras theorem. Then add the base of the tree and the hypotenuse, the resultant value will be the original height of the tree.

Pythagoras theorem states that :

• The sum of the square of the two sides, i.e. the base and the perpendicular is equal to the square of the third longest side of the right angled triangle, i.e. hypotenuse.

Mathematically,

• H² = P² + B²

where,

• H = Hypotenuse (longest side)
• P = Perpendicular (the side of the triangle on which the angle of 90° is there)
• B = Base of the triangle

Solution :

we have,

• Perpendicular (AB) = 5 m
• Base (BC) = 12 m
• Hypotenuse (AC) = ?

Using pythagoras theorem,

↠ AC² = AB² + BC²

↠ AC² = (5)² + (12)²

↠ AC² = 25 + 144

↠ AC² = 169

Taking square root on both the sides.

↠ AC = √169

↠ AC = √(13 × 13)

↠ AC = ± 13

As we know, side of the triangle cannot be negative. So, the negative sign will get rejected.

↠ AC = ± 13 Reject - ve

↠ AC = 13

The value of AC = 13 m

→ Original height of the tree = AB + AC

→ Original height of the tree = 5 + 13 = 18

Therefore,

• The original height of the tree = 18 m

Answer 2

Given :- A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

Answer :-

as the tree broken at a height of 5 m from ground and its top touches at a distance of 12 m . we can conclude that, 5 m is perpendicular height and 12m is base distance .

so, using pythagoras theorem we get,

→ Broken part lenth of tree = √(Height)² + (Base)² = √(5)² + (12)² = √25 + 144 = √169 = 13 m .

then,

→ Original height of tree = height from ground + broken part = 5 + 13 = 18 m (Ans.)

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