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 12m from ground. If the tree leans of B's house, the tree top rests on his window which is 9m from ground. If the height of the tree is 15m, what is distance between A's and B's house?
(Geometry - Triangle)

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

Let us draw a figure according to question

Here, $△$ PQT is a right angled-triangle,

So, we can write from Pythagorean Theorem:

$P T^{2} = P Q^{2} + Q T^{2} = Q T^{2} = P T^{2} - P Q^{2} = 15^{2} - 9^{2} = 225 - 81 = 144 ∴ Q T = \sqrt{144} = \sqrt{{(12)}^{2}} = 12 m e t e r H e r e, △ T R S i s a l s o a r i g h t a n g l e d t r i a n g l e, s o w e c a n w r i t e f r o m P y t h a g o r e a n T h e o r e m : {(T S)}^{2} = {(T R)}^{2} + {(S R)}^{2} = {(T R)}^{2} = {(T S)}^{2} - {(S R)}^{2} = 15^{2} - 12^{2} = 225 - 144 = 81 ∴ T R = \sqrt{81} = \sqrt{{(9)}^{2}} = 9 m e t e r H e r e, d i s \tan c e b e t w e e n h o u s e s i s Q R Q R = Q T + T R ∴ Q R = 12 + 9 = 21 m e t e r ∴ D i s \tan c e 21 m e t e r (a n s w e r)$