Question

plz solve this question​

Answer 1

Step-by-step explanation:

(i) Consider △ ABC

We know that

AB + BC > AC …… (1)

Consider △ ACD

We know that AD + CD > AC ……. (2)

By adding both the equations we get

AB + BC + AD + CD > AC + AC

So we get

AB + BC + AD + CD > 2AC …….. (3)

Therefore, it is proved that AB + BC + AD + CD > 2AC.

(ii) Consider △ ABC

We know that

AB + BC > AC

Add CD both sides of the equation

AB + BC + CD > AC + CD …… (4)

Consider △ ACD

We know that

AC + CD > DA ……. (5)

By substituting (5) in (4) we get

AB + BC + CD > DA …….. (6)

(iii) Consider △ ABD and △ BDC

We know that

AB + DA > BD ……. (7)

So we get BC + CD > BD ……. (8)

By adding (7) and (8) we get

AB + DA + BC + CD > BD + BD

On further calculation

AB + DA + BC + CD > 2BD ……. (9)

By adding equations (9) and (3) we get

AB + DA + BC + CD + AB + BC + AD + CD > 2BD + 2AC

So we get

2 (AB + BC + CD + DA) > 2 (BD + AC)

Dividing by 2

AB + BC + CD + DA > BD + AC

Therefore, it is proved that AB + BC + CD + DA > BD + AC.

hope it will help you.

Answer 2

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Harshita

class 8th