Question 13

If the perimeters of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1 : 2 then the ratio of area of the rectangle and that of the square is

Solution

let l, b are the length & breadth of a rectangle, and s be the side of a square.

l:b = 2:1 so l = 2b.

given that perimeters of both are same,

2(l+b) = 4s

2(2b+b) = 4s

6b = 4s

b/s = 2/3

area of rectangle = l*b = 2b*b = 2$$b^{2}$$

area of square = $$s^{2}$$

ratio = (2$$b^{2}$$)/($$s^{2}$$)

= 2$$(b/s)^{2}$$

= 2(4/9) = 8/9 = 8 : 9

so the answer is option D.

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