Question : One of the diagonals of a rhombus is 70 percent of the other diagonal. What is the ratio of the area of the rhombus to the square of the length of the larger diagonal?
Option 1: 5 : 17
Option 2: 7 : 20
Option 3: 6 : 19
Option 4: 20 : 7
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Correct Answer: 7 : 20
Solution : Let the diagonals of the rhombus are $d_1=x$ and $d_2=0.7x$ So, the area of the rhombus = $\frac{1}{2}× x× 0.7x$ Now, let's find the ratio of the area of the rhombus to the square of the length of the larger diagonal: Area of square = $x^2$ Required ratio = $\frac{\frac{1}{2}× x× 0.7x}{x^2}$ =$\frac{7}{20}$ Hence, the correct answer is 7 : 20.
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