Final answer:
The base and height of the triangle with a given area of 43.2 m² and a ratio of 5:3 are found by expressing them as 5x and 3x, respectively, and solving for x using the area formula for a triangle. The base is 12 meters and the height is 7.2 meters.
Step-by-step explanation:
To find the base and the height of the triangle with a given area and ratio, we use the formula for the area of a triangle: Area = 1/2 × base × height.
Given that the ratio of the base to the height is 5:3, let the base be 5x and the height be 3x.
Plugging these into the area formula, where the area is 43.2 m², we get:
43.2 = 1/2 × (5x) × (3x)
Multiplying through and dividing both sides by 1.5 (the product of 1/2 and 3), we get:
43.2 = 7.5x²
x² = 43.2 ÷ 7.5 = 5.76
x = √5.76 = 2.4
Now, we can find the base and the height:
Base = 5x = 5 × 2.4 = 12 m
Height = 3x = 3 × 2.4 = 7.2 m
Therefore, the base of the triangle is 12 meters and the height is 7.2 meters.