Two sides of a triangle are 6 cm and 8 cm. If the height of the triangle corresponding to 6 cm side is 4 cm; find :

(i) area of the triangle

(ii) height of the triangle corresponding to 8 cm side.

(i) Given:

Side of the triangle = 6 cm

Height of the triangle = 4 cm

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

= $\dfrac{1}{2}$ x 6 x 4 cm²

= $\dfrac{1}{2}$ x 24 cm²

= 12 cm²

Hence, area of triangle = 12 cm².

(ii) When, the side of the triangle = 8 cm

Let the height of the triangle be h cm

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

= $\dfrac{1}{2}$ x 8 x h ²

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

⇒ $\dfrac{1}{2}$ x 8 x h = 12

⇒ 4 x h = 12

⇒ h = $\dfrac{12}{4}$

⇒ h = 3 cm

Hence, height of the triangle corresponding to 8 cm side is 3 cm.