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Geometry/Direct and Inverse Variation


Hello sir

sir i am asking a question of direct and inverse variation . I know sir that it little much related to algebra.

Sir the question is A tree of 14m height cast a shadow of 10 m. find the height of the tree that  caste  a shadow of 15m at the same time.

Sir in solution it is given that it is direct variation  onthis basis" The more height  of an object , the more would be lenght of its shadow.

But Sir see sir in this situation the height of a tree is is more that its lenght of its shadow then how sir the more height of an object , the more would be  the lenght or it is direct varition it should be inverse variation becase here one value is decreased and one is increased and this is in inverse variation.

Sir in this iam confused so iam asking i have askedin detail and in clear

Hi Aishwaraymeti,

"The greater the height of an object, the longer its shadow will be."  If this does not make sense intuitively, let me know.  Frankly, this problem might be easier if you do not think of it in terms of inverse/direct variation.

This is, in essence a question of similar triangles (if you don't understand what I mean, let me know).  Assuming the tree is perpendicular to the ground, we can view this as a right triangle with height 14m and base 10m.

The tree that casts a longer shadow will be a different, but similar triangle ("at the same time" implies the angle of the sun is the same).  The corresponding dimensions of similar figures share a common ratio.  Suppose we had a small triangle with base b and height h, and a large triangle with base capital B and height capital H.  Provided the triangles are similar, we will always have the following relation:

h/b = H/B

In your particular question, we would have 14/10 = H/15, from which you can solve for H.

Thanks for asking,


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Azeem Hussain


I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.


4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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