Question
The diagonals of a rhombus are in the ratio 7:5, and its
area is 3,500 cm². A circle is formed taking the smaller diagonal as the diameter. Find the difference between the area of the circle and three-fourths of the area of the rhombus. (Take π = 3)Solution
ATQ,
Let diagonals = 7x and 5x
Area = (1/2) × 7x × 5x = 17.5x²
3500 = 17.5x² → x² = 200 → x = √200 ≈ 14.14
Smaller diagonal = 5x ≈ 70.7 cm
Radius ≈ 35.35 cm
Area of circle ≈ 3 × (35.35)² ≈ 3 × 1249.7 ≈ 3749.1 cm²
75% of rhombus = 0.75 × 3500 = 2625 cm²
Difference ≈ 3749.1 - 2625 = 1124.1 cm²
When the digits are swapped, the new two-digit number equals 44 less than 120% of the original. The sum of the digits is 13. Determine the original number.
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