The base and the height of a triangle are in the ratio 5 : 3. If the area of the triangle is 67.5 m²; find its base and height.

Given:

The base and the height of a triangle are in the ratio 5 : 3.

The area of the triangle = 67.5 m²

Let the base of the triangle = 5x m

And, the height of the triangle = 3x m

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

⇒ $\dfrac{1}{2}$ x 5x x 3x = 67.5 m²

⇒ $\dfrac{1}{2}$ x 15x² = 67.5 m²

⇒ 15x² = 2 $\times$ 67.5 m²

⇒ 15x² = 135 m²

⇒ x² = $\dfrac{135}{15}$ m²

⇒ x² = 9 m²

⇒ x = $\sqrt{9}$ m

⇒ x = 3 m

So, base of the triangle = 5x

= 5 x 3 m

= 15 m

And, height of the triangle = 3x

= 3 x 3 m

= 9 m

Hence, base and height of the triangle are 15 m and 9 m, respectively.