Question

32. Oisapoint in the exiorior of AC, themprove thu OA OB OC> (AB-BC-CA)​

Answer 1

Step-by-step explanation:

We know that AB < AO + BO ( Sum of 2 sides of triangle is greater than 3)

similarly AC < AO + CO ( Sum of 2 sides of triangle is greater than 3)

BC < BO + CO ( Sum of 2 sides of triangle is greater than 3)

Now adding all LHS and RHS we get

⇒ AB + AC + BC < AO + BO + AO + CO + BO + CO

⇒ AB + AC + BC < 2AO + 2BO + 2CO

⇒ AB + AC + BC < 2(AO + BO + CO)

⇒ 1/2(AB + AC + BC) < AO + BO + CO

∴AO + BO + CO > 1/2(AB + AC + BC).

Answer 2

Answer:

Let breadth(b)=x m

l=2.5 m, h=10 m

V=l×b×h=(2.5×x×10)m3

=25x m3

Capacity of a tank =25x m3=50000 litres

⇒25x m3=50 m3

⇒x=2

Hence, b=2 m.