CBSE Class 10 Answered

Let the three angles be a-d, a, a + d.

By angle sum property, 3a = 180⁰

⇒ a = 60⁰

So, the possible combination for three angles to be in AP are either 60⁰, 60⁰, 60⁰ or 30⁰, 60⁰, 90⁰.

But the combination 60⁰, 60⁰, 60⁰ does not hold for this triangle since the two sides are 10cm and 8 cm which implies that the three angles of the triangle are unequal.

So, the angles are 30⁰, 60⁰, 90⁰

This implies that the sides are pythagorian triplet.

Using pythagoras theorem,

we get the third side   = (10)² - (8)² = 6cm.

Hence the answer.