Question 37

Perimeter of a rectangle is x and circumference of a circle is 8 more than the perimeter of the rectangle. Ratio of radius of circle and length of the rectangle is 1:2 and ratio of length and breadth of rectangle is 7:3. Find the length of the rectangle ?

Solution

Perimeter of rectangle = x

Perimeter of circle =x+8

Given that radius/length = 1/2

So radius = y and length = 2y

Now it is also given that length/breadth = 7/3

So length = 7m and breadth = 3m

Here we can say that 7m = 2y as both are length of same rectangle

Perumeter of rectangle = 2 (7m+3m) = 20m

Circumference of circle = 2πR = 2× 3.14× y = 20m +8

M = 4

Hence length if rectangle = 7×4 =28

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