Question

In the given figure, prove that

(i) CD + DA + AB > BC

(ii) CD + DA + AB + BC > 2AC.

Answer 1

(i) Consider △ CDA

We know that CD + DA > AC ….. (1)

Consider △ ABC

We know that AC + AB > BC ….. 21)

By adding both the equations we get

CD + DA + AC + AB > AC + BC

By subtracting AC on both the sides

CD + DA + AC + AB – AC > AC + BC – AC

So we get

CD + DA + AB > BC

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

(ii) Consider △ CDA

We know that CD + DA > AC ….. (1)

Consider △ ABC

We know that AB + BC > AC ….. (2)

By adding both the equations we get

CD + DA + AB + BC > AC + AC

So we get CD + DA + AB + BC > 2AC

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