The base of an isosceles triangle is 16 cm and its area is 48 cm². The perimeter of the triangle is :

1. 24 cm

2. 30 cm

3. 36 cm

4. 42 cm

From figure,

ABC is an isosceles triangle with AM as the height and BC as the base.

Base (BC) = 16 cm

Area of triangle = $\dfrac{1}{2}$ × base × height

⇒ 48 = $\dfrac{1}{2}$ × 16 × AM

⇒ 48 = 8 × AM

⇒ AM = $\dfrac{48}{8}$ = 6 cm.

In an isosceles triangle,

The altitude from the common vertex bisects the base.

In triangle ABC,

The altitude AM bisects the base BC.

So, BM = MC = $\dfrac{BC}{2} = \dfrac{16}{2}$ = 8 cm.

Using Pythagoras theorem for the △AMB,

Hypotenuse² = Base² + Height²

⇒ AB² = BM² + AM²

⇒ AB² = 8² + 6²

⇒ AB² = 64 + 36

⇒ AB² = 100

⇒ AB = $\sqrt{100}$ = 10 cm.

∴ AC = AB = 10 cm.

Perimeter of triangle = Sum of all sides of the triangle

= AB + AC + BC

= 10 + 10 + 16 = 36 cm.

Hence, option 3 is the correct option.