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Prove that the perimeter of a triangle i...

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

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Given : ABC is a triangle in which AD, BE and CF are perpendiculars.
To Prove : `AB+BC+CA gt AD+BE+CF`
Proof : Since in a right angled triangle, hypotenuse is the longest side.
`:.` In right `DeltaABD, " "AB gt AD` ...(1)
(side opposite to greater angle is longer)
In right `DeltaBEC," "BC gt BE` ...(2)
(side opposite to greater angle is longer)
In right `DeltaAFC," "AC gt CF" "`(side opposite to greater angle is longer) ...(3)
Adding (1), (2) and (3), we get
`AB+BC+CA gt AD + BE+ CF` Hence Proved.
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