The length and the breadth of a rectangle are 12 cm and 9 cm respectively. Find the height of a triangle whose base is 9 cm and whose area is one-third that of rectangle.

Area of rectangle = l × b = 12 × 9

= 108 cm².

Given,

Area of triangle = one-third the area of rectangle.

Substituting the values we get,

Area of triangle = $\dfrac{1}{3}$ × 108 = 36 cm².

Consider h cm as the height of triangle.

By formula,

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

Substituting the values we get,

⇒ 36 = $\dfrac{1}{2}$ × 9 × h

⇒ 36 × 2 = 9 × h

⇒ h = $\dfrac{72}{9}$

⇒ h = 8 cm.

Hence, height of triangle is 8 cm.