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Prove that the sum of three …

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Prove that the sum of three altitudes is less than the perimeter of a triangle.

    • Posted by Kittu Nagar 2 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Shanu Pratap 2 years, 3 months ago

    Let ABC be the △ with sides BC,AC and AB opposite to the angles A,B and C being in length equal to a,b and c respectively. To prove:- AL+BM+CN<AB+BC+CA Construction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively. Now, In △ACL, Using pythagoras theorem, AC2=AL2+CL2 ⇒AC2>AL2 ⇒AC>AL.....(1) Similarly, AB>BM.....(2) BC>CN.....(3) Adding equation (1),(2)&(3), we get] AB+BC+AC>AL+BM+CN Hence proved.

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