Option 2 : 10 cm

Given

Altitude of the triangle = 12 cm

Perimeter of triangle = 36 cm

Concept Used

Altitude of triangle = √[(Equal sides)2 - (Base/2)2]

Perimeter of triangle = 2 × Equal sides + base

Calculation

Let the length of equal sides be x and base side be y

Altitude of triangle = √[(Equal sides)2 - (Base/2)2]

⇒ 12 = √(4x2 - y2)/4

⇒ 4x2 - y2 = 144 × 4

⇒ 4x2 – y2 = 576 ----(i)

Perimeter of triangle = 2 × Equal sides + base

⇒ 2x + y = 36 ----(ii)

From (i) and (ii) we get,

⇒ x = 13, y = 5

So, BC = 2 × 5 = 10 cm

__Alternate Method__

Altitude = 12 cm

We know the triplet 5, 12, 13

In ΔADC, AD is an altitude which is equal to 12 cm

So, AC = 13 cm and CD = 5 cm

We know in the isosceles triangle, altitude is the same as the median

So, BC = 2 × 5 = 10 cm

∴ The required answer is 10 cm