The base and the height of a triangle are in the ratio 4 : 5. If the area of the triangle is 40 m², find its base and height.

Given:

The base and the height of a triangle are in the ratio 4 : 5.

The area of the triangle = 40 m²

Let the base of the triangle be 4x m.

And, the height of the triangle be 5x m.

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

⇒ $\dfrac{1}{2}\times$ 4x $\times$ 5x = 40 m²

⇒ $\dfrac{1}{2}\times$ 20x² = 40 m²

⇒ 10x² = 40 m²

⇒ x² = $\dfrac{40}{10}$ m²

⇒ x² = 4 m²

⇒ x = $\sqrt{4}$ m

⇒ x = 2 m

So, base of the triangle = 4x

= 4 x 2 m

= 8 m

And, height of the triangle = 5x

= 5 x 2 m

= 10 m

Hence, base and height of the triangle are 8 m and 10 m, respectively.