Question

In a quadrilateral ABCD, the side and diagonals are related as
a) AB + BC + CD + DA < AC + BD
b) AB + BC + CD + AD > AC + BD
c) AB + BC + CD + DA = AC + BD
d) AB + BC + CD = AC - BD​

Answer 1

Answer:

AC+BD < AB+BC+CD+AD

option (b) is correct

Step-by-step explanation:

In ΔABC,

we have AC < AB+BC

In ΔACD

we have, AC < AD+CD

Adding these inequalities we get

2 AC < AB+BC+CD+AD......(1)

In ΔABD,

we have BD < AB+AD

In ΔBCD

we have, BD < BC+CD

Adding these inequalities we get

2 BD < AB+BC+CD+AD......(2)

Now adding (1) and (2)

2(AC+BD) < 2(AB+BC+CD+AD)

divided by 2

AC+BD < AB+BC+CD+AD

Answer 2

It may help you

♡Thank you♡