Question

The diagonals of two squares are in ratio 3 ratio 2. Find the ratio of their areas

Answer 1

Answer:

9 : 4

Step-by-step explanation:

if diagonals of a SQUARE are in ratio 3:2 then sides would also be in the same ratio

so area will be in $3^{2}:2^{2}$ ratio

i.e 9:4

Answer 2

Given :  diagonals of two squares are in ratio 3 ratio 2

To Find : ratio of their areas

Solution:

Let say Diagonal of  squares are 3A and 2A

Diagonals of Squares are Equal

Square is also a rhombus

Area of rhombus = (1/2) * d₁ x d₂

d₁ = d₂ in square

= (1/2) (diagonal)²

Diagonal of  squares is 3A  Then Area = (1/2) (3A)² = 9A²/2

Diagonal of  squares is 2A  Then Area = (1/2) (4A)² = 4A²/2

Ratio of Areas  = 9A²/2 : 4A²/2

= 9 : 4

Ratio of Areas  =9:4

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