the diagonals of two squares are in the ratio 3 : 7 . find the ratio of their areas ?
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Given : diagonals of two squares are in ratio 3:7
To Find : ratio of their areas
Solution:
Let say Diagonal of squares are 3A and 7A
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 7A Then Area = (1/2) (7A)² = 49A²/2
Ratio of Areas = 9A²/2 : 49A²/2
= 9 : 49
Ratio of Areas =9:49
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