Q14 of 99 Page 269

The length of a rhombus is equal to length of a square and the length of diagonal of square is 10√2 cm. If the length of diagonals of a rhombus are in the ratio 3 : 4, then let us write by calculating the area of a field in the shape of rhombus.

Given, The length of a rhombus is equal to length of a square and the length of diagonal of square is 10√2 cm and the length of diagonals of a rhombus are in the ratio 3 : 4

The diagonal of a square = a


10 = a


a = 10cm


i.e. the side of the square = 10 cm


according to given question side of the rhombus is equal to the side of the square


∴ side of the rhombus = 10 cm


The diagonals of a rhombus bisect each other. Let the diagonals are 3x and 4x.


Hence, 102 = (3x)2 + (4x)2


⟹ 102 = 25x2


⟹ X2 = 4


⟹ X = 2


∴ the diagonals are, 3x = 3×2


= 6cm


And, 4x = 4×2


= 8cm


The area of the rhombus = ×6×8


= 24 sq. cm.


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