Question

Justify the following statement with reasons: The sum of three sides of a triangle is more than the sum of its altitudes.

Answer 1

In ∆ABC ,

AD , BE and CF are altitudes of BC,

CA and AB respectively .

i ) In Right ∆ADB , <ADB = 90°

AB > AD ------( 1 )

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Side opposite to larger angle is larger .

Or

In right angled triangle hypotenuse has

Heighest length.

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ii ) In right ∆BEC , <BEC = 90°

BC > BE -----( 2 )

iii ) In ∆AFC , <AFC = 90°

AC > CF -----( 3 )

Add ( 1 ) , ( 2 ) and ( 3 ), we get

( AB + BC + AC ) > ( AD + BE + CF )

Therefore ,

Sum of three sides of triangle is greater

than sum of its altitudes .

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