Answer:
The ratio of the perimeters of the two trapezium is 2
The ratio of the corresponding sides of the two trapezium is 2
Explanation:
The given parameters in the question are;
Two trapeziums are similar
The area of one trapezium = 4 × The area of the other trapezium
Let, A₁, and A₂ represent the area of the two trapeziums, we have
A₁ = 4 × A₂
∴ A₁/A₂ = 4
Given that ratio of areas = (Ratio of sides)²
Ratio of sides = Ratio of perimeter
∴ Ratio of areas = (Ratio of perimeter)²
Therefore, given that the ratio of the areas of the two trapeziums A₁/A₂ = 4, we have;
Ratio of areas = 4 = (Ratio of sides)²
The ratio of the corresponding sides = √4 = 2
The ratio of the corresponding sides = 2
Ratio of areas = 4 = (Ratio of perimeter)²
The ratio of the perimeter = √4 = 2
The ratio of the perimeter = 2