Question

4) There is a tree between houses of A and B. If the
tree leans on A's House, the tree top rests on his
window which is 12 m from ground. If the tree leans
on B's House, the tree top rests on his window which
Is 9 m from ground. If the height of the tree is 15 m,
what is distance between A's and B's house?​

Answer 1

Given : -

There is a tree between houses of A and B. If the tree leans on A's House, the tree top rests on his window which is 12 m from ground. If the tree leans on B's House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m.

Required to find : -

• Distance between the 2 houses ?

Pythagoran theorem : -

This theorem is only applicable in right angled triangles !

The theorem is stated as ;

The sum of the square of the sides of right angled triangle is equal to the square of the hypotenuse .

Represented as ,

( side )² + ( side )² = ( hypotenuse )²

Solution : -

There is a tree between houses of A and B. If the tree leans on A's House, the tree top rests on his window which is 12 m from ground. If the tree leans on B's House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m.

We need to find the distance between the 2 houses .

Refer to the attachment <=

By referring the attachment we can conclude that ;

AB = Height of the tree = 15 cm

EB = The slanting of the tree on house A

BF = The slanting of the tree on house B

EC = FD = 15 cm

( Reason : The tree rests on house A's window which is 12 m from ground , Similarly, in case of B it rests 9 meters ground )

CD = Distance between the 2 houses

Here,

We can see 2 right angled triangles .

i.e ∆ BCD & ∆ BDF

In ∆ BCD ,

∠BCD = 90° . So, ∆ BCD is a right angled triangle.

Pythagoran theorem is applicable here !

Using the Pythagorean theorem ;

➟ ( side )² + ( side )² = ( hypotenuse )²

➟ ( 12 )² + CB² = ( 15 )²

➟ 144 + CB² = 225

➟ CB² = 225 - 144

➟ CB² = 81

➟ CB = √81

➟ CB = ± 9 meters

Since, length can't be in negative .

Hence,

• Length of CE = 9 meters

Similarly,

In ∆ BDF ,

∠BDF = 90° , So ∆ BDF is a right angled triangle .

Pythagoran theorem is applicable here !

Using the Pythagorean theorem ,

➟ ( side )² + ( side )² = ( hypotenuse )²

➟ ( BD )² + ( DF )² = ( BF )²

➟ BD² + ( 9 )² = ( 15 )²

➟ BD² + 81 = 225

➟ BD² = 225 - 81

➟ BD² = 144

➟ BD = √144

➟ BD = ± 12 meters

Since, length can't be in negative .

So,

• Length of BD = 12 meters

Here , we need to apply a bit of logic.

As we know that ;

CD is the distance between the two houses .

➟ CD = CB + BD

➟ CD = 9 + 12

➟ CD = 21 meters

Therefore,

➟ The distance between the 2 houses is 21 meters .