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
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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