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Sum of perimeter of two rectangles is 248 cm and breadth of both rectangles is equal to radius of circle whose circumference is 44 cm. If length of both rectangles is in the ratio of 9 : 13, then find the difference between areas of both rectangles?

Sum of perimeter of two rectangles is 248 cm and breadth of both rectangles is equal to radius of circle whose circumference is 44 cm. If length of both rectangles is in the ratio of 9 : 13, then find the difference between areas of both rectangles? Correct Answer 140 cm

GIVEN :

Sum of perimeter of two rectangles is 248 cm

Circumference of circle = 44 cm

Ratio of lengths of both the rectangles = 9 : 13

 

FORMULA USED :

Circumference of circle = 2πr

Perimeter of rectangle = 2 × (length + breadth)

Area of rectangle = length × breadth

 

CALCULATION :

Let the length of rectangles be 9x and 13x

Circumference of circle = 2πr = 44

⇒ r = 7

Breadth of rectangle = radius of circle

According to question,

Sum of perimeter of two rectangle = 248 cm

⇒ 2 (9x + 7) + 2 (13x + 7) = 248

⇒ 18x + 14 + 26x + 14 = 248

⇒ 44x + 28 = 248

⇒ 44x = 220

⇒ x = 5

⇒ Length of rectangles = 9 × 5 = 45 cm and 13 × 5 = 65 cm

⇒ Difference between areas = 65 × 7 – 45 × 7 = 140 cm2

∴ Required difference = 140 cm2

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