Question

6. In triangle ABC, given below, AB = 8 cm,
BC = 6 cm and AC = 3 cm. Calculate the
length of OC.​

Answer 1

Step-by-step explanation:

Give that

In triangle ABC, AB = 8 cm,

BC = 6 cm and AC = 3 cm

OC=?

In the figure angle AOC =90°

So,triangle AOC & triangle ABO are right angle triangle.

In ∆ AOC, applying Pythagorean triple

we get AC² = AO²+OC²

So, 9=AO²+OC²••••••••••(i)

In ∆ AOB,applying Pythagorean triple

we get AB²= AO²+BO²

So, 64 = AO²+ (BC+CO)²

=> 64=AO² + (6+CO)²

=>64= AO²+[36+ CO²+ 12×CO]

=>64-36=AO²+CO²+12CO

=>28= AO²+OC²+12CO•••••••••(ii)

Applying the value of equation (i) in equation (ii)

we get,

28 = 9 + 12CO

=>28 - 9 = 12CO

=>19 = 12CO

=>CO=19/12 cm. Ans