A rhombus has one of its diagonal 65% of the other. A square is drawn using the longer diagonal side. What will be the ratio of the area of the rhombus to that of the square?

Correct option is B

Given:

A rhombus has one of its diagonal 65% of the other.

A square is drawn using the longer diagonal as a side.

Formula used:

Area of rhombus = $$\frac{1}{2}$$​(diagonals product)

Area of square = side × side

Solution:

Let larger diagonal of rhombus be 100 cm.

then smaller diagonal will be 65 cm (65% of larger diagonal)

Area of Rhombus = $$\frac{1}{2}$$​(100 × 65) = 3250

Now, side of square = larger diagonal

Side of square = 100 cm 

Area of square = (100 × 100) = 10000

then Ratio of area of rhombus to area of square is 

=> Rhombus : Square = 3250 : 10000

=> 13 : 40

Hence, option (b) is the correct answer.