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Answer»

Please keep drawing the figure as you follow below.Let ABC be the triangle with sides BC, AC, AB opposite angles A, B, Cbeing in lengthequal to a, b, c respectively.

Draw perpendiculars AD, BE and CF from A, B, C to opposite sides meeting sides BC, AC and AB at D, E, F respectively.

Now perpendicular AD² = AC² - CD² ==> AD² < AC² or AD < AC or AD < b-----(1) Also, BE²= AB² - AE² ==> BE² < AB² or BE < AB or BE < c ------(2) Likewise , CF² = BC² - BF² ==> CF² < BC² or CF < BC or CF < a ----(3)Adding inequalities (1), (2), (3), AD + BE + CF < a + b + c


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