Question
A circular wire of diameter 84 cm is folded in the shape
of a rectangle whose sides are in the ratio 8:3. Find the area enclosed by the rectangle.Solution
Using the formula, Area = lb & D = 2r and A = πr² Radius of circular wire = 84/2 = 42 cm Circumference of wire = 2πr = 2 x (22/7) x 42 = 264 cm Let the length and breadth of rectangle be 8x & 3x cm respectively. Therefore, perimeter of rectangle = 2(8x + 3x) = 22x According to the question, 22x = 264 ⇒ x = 264/22 = 12 Therefore, length of rectangle = 8x = 8 x 12 = 96 cm Breadth of rectangle = 3x = 3 x 12 = 36 cm Area = 96 x 36 = 3456 cm²
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