Question

ABCD is a quadrilateral.

Is AB + BC + CD + DA > AC + BD?​

Answer 1

Answer:

We know that,

The sum of the length of any two sides is always greater than the third side.

Now consider the ΔABC,ΔABC,

Here, AB + BC > CAAB+BC>CA … [equation i]

Then, consider the ΔBCDΔBCD

Here,BC + CD > DBBC+CD>DB … [equation ii]

Consider theΔCDAΔCDA

Here, CD + DA > ACCD+DA>AC … [equation iii]

Consider the ΔDABΔDAB

Here, DA + AB > DBDA+AB>DB … [equation iv]

By adding equation [i], [ii], [iii] and [iv] we get,

AB + BC + BC + CD + CD + DA + DA + AB > CA + DB + AC + DBAB+BC+BC+CD+CD+DA+DA+AB>CA+DB+AC+DB

→2AB + 2BC + 2CD + 2DA > 2CA + 2DB→2AB+2BC+2CD+2DA>2CA+2DB

Take out 2 on both the side,

→2(AB + BC + CA + DA) > 2(CA + DB)→2(AB+BC+CA+DA)>2(CA+DB)

→AB + BC + CA + DA > CA + DB→AB+BC+CA+DA>CA+DB

Hence, the given expression is true.

Answer 2

Answer:

Refer to the attachment above. ⬆️

hope it helps!!