Two sides of a triangle are 12 cm and 15 cm. If the height of the triangle corresponding to 12 cm side is 10 cm, then the height of the triangle corresponding to 15 cm side is:

1. 4 cm

2. 12 cm

3. 8 cm

4. 16 cm

Given:

Sides of the triangle = 12 cm, 15 cm

Height of the triangle = 10 cm

As we know, the area of the triangle = $\dfrac{1}{2}$ x side x height

= $\dfrac{1}{2}$ x 12 x 10 cm²

= $\dfrac{1}{2}$ x 120 cm²

= 60 cm²

When, side of the triangle = 15 cm

Let the height of the triangle = h cm

As we know, the area of the triangle = $\dfrac{1}{2}$ x side x height

= $\dfrac{1}{2}$ x 15 x h ²

[∵ Both areas remain same since they represent the area of the same triangle.]

⇒ $\dfrac{1}{2}$ x 15 x h = 60

⇒ 15 x h = 2 x 60

⇒ 15 x h = 120

⇒ h = $\dfrac{120}{15}$

⇒ h = 8 cm

Hence, the height of the triangle corresponding to 15 cm side is 8 cm.

Hence, option 3 is the correct option.