Question
Perimeter of a rectangle is x cm and circumference of a
circle is (x + 6) cm. The length of the rectangle is ______ cm. The ratio of the radius of the circle and the length of the rectangle is 1:2 and ratio of length and breadth of the rectangle is 7:3.Solution
Let the length and breadth of the rectangle be 7a cm and 3a cm respectively. Perimeter of rectangle = 2 (7a + 3a) = 20a Radius of circle/Length of rectangle = 1/2 ⇒ r/7a = 1/2 According to the question ⇒ 2 π r – 20a = 6 ⇒ 2 x 22/7 x 7a/2 – 20a = 6 ⇒ 22a – 20a = 6 ⇒ 2a = 6 ⇒ a = 3  Length of the rectangle = 7 x 3 = 21 cm
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