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Hello sir

Sir i searched in internet that Are there rectangles whose diagonals are perpendicular and equal in length? Yes, these are the special rectangles called squares - . Sir i have an confusion that if diagnals of recatangle are eqaul in lenght but lenght of rectangle are not equal in lenght , then how they can be called as sqaues.

Sir hope it is clear.

Hi Shilpa,

If the diagonals of a rectangle are equal and perpendicular, then the sides of the rectangle will be equal also, and the rectangle will indeed be a special rectangle: a square.

It is possible that the diagonals of the rectangle be equal and NOT perpendicular, in which case you will have a rectangle that is not a square.

So in short, if you have a rectangle AND the diagonals are equal, then it MUST be a square.

(If you would like an explanation as to why this is true, think about it for a bit, then ask a follow-up if you need.)

Hope this is clear,

Azeem

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

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