Question

The base and the height of a triangle are in the ratio of 5:3 and it’s area is 43.2 m^2 .Find the base and the height of the triangle

Answer 1

Given:

• Ratio of base and height of triangle = 5:3
• Area = 43.2m²

To Find:

• Height and base of the triangle.

Solution:

Here, we have to find the base and height if the triangle. We have given the measures in ratio.

Let the height of base of the triangle be 5x and height be 3x.

Substituting Formula:

⇛ Area of triangle = 43.2m²

⇛ 1/2 × base × height = 43.2

⇛ 1/2 × 5x × 3x = 43.2

⇛ 1/2 × 15x² = 43.2

⇛ x² = 43.2 × 2 / 15

⇛ x² = 432 ×2/ 15×10 (As the decimal is removed)

⇛ x² = 57.6 / 10

⇛ x² = 576/100 ( Decimal is again removed)

⇛ x = √576/100

⇛ x = 24/10

⇛ x = 2.4

So, we got the value of 'x' as 2.4. We will not substitute5x the values and find height and base.

Base = 5x = 5×2.4 = 12cm

Height = 3x = 3×2.4 = 7.2 cm

So, base and height of the triangle are 12 and 7 cm respectively.