Question

answer this question with step by step explanation class 7 And who ever will give me the correct answer I will mark him or her as brainlist​ ​

Answer 1

Answer:

please mark as brainiest

Step-by-step explanation:

Please keep drawing the figure as you follow below.

Let ABC be the triangle with sides BC, AC, AB opposite angles A, B, C being in length equal 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

Answer 2

In Δ ABD,

< D=90º and < B is acute

< D > < B

•'•AB >AD... (1)

.

| side opposite to greater angle is longer in △ ACD,

< D=90º and < C is acute.

•`• Ac >AD... (2)

|side opposite to greater angle is longer adding

(1) and (2), we have AB+AC > 2AD... (3)

Similarly, we can prove that, BC +BA >2CF... (5)

|•.•CF π AC Adding (3),(4) and (5),weget

=>2(AB+BC+CA) >2 (AD+BE+CF)

=>AB+BC+CA>AD+BE+CF

=>AD+BE+CF<AB+BC+BC+CA.