Question

3. If the perimeters of a rectangle and a square are equal and the ratio of the two adjacent sides of the rectangle is 1:2 then the ratio of area of the rectangle and that of the square is.
(a) 1:1
(b) 1:2
(c) 2:3
(d) 8:9
ANSWER FAST​

Answer 1

Given that :

perimeter of the rectangle and square are equal.

side of the rectangle is 1:2.

to find:

ratio of area of the rectangle and the square

solution:

perimeter of the rectangle = 2(l+b)

perimeter of the square = 4 × sides

=>

$\frac{l}{b} = \frac{1}{2}$

or

l = x

b = 2x

=>

$\frac{3x}{2}$

=>

$\frac{area \: of \: rectangle}{area \: of \: square}$

=

$\frac{x \times 2x}{3by2 x \: {}^{2} }$

$\frac{8}{9}$

= 8.9

hence the required answer is :

$\boxed{ \frac{8}{9} }$