Question
The length of a rectangle is 64 cm. If the ratio of
length to perimeter of the rectangle is 4:15, find the area of a circle whose diameter is 6 cm less than double the breadth of the rectangle. (Take π = 22/7)Solution
ATQ; Perimeter of rectangle = 2 × (length + breadth) So, 64 : [2 × (64 + breadth)] = 4 : 15 Or, 15 × 64 = 4 × 2 × (64 + breadth) Or, 960 = 8 × (64 + breadth) Or, 64 + breadth = 120 Or, breadth = 56 cm Diameter of circle = 2 × 56 - 6 = 106 cm Radius of circle = 106 ÷ 2 = 53 cm Area of circle = π × radius² = (22/7) × 53² = (22/7) × 2809 = 8,828 cm²
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