Question

If the length of a rectangle is reduced by 50% and the breadth is increased by 25%, it takes the
shape of a square. Find the ratio of the areas of the rectangle and the square, and the perimeters of the rectangle and the square.​

Answer 1

for the rectangle let :

length =x     and     breadth=y

the area of the rectangle (A) : A=x*y

the perimeter of the rectangle (P): P=(x+y)*2

then for the square

length =(1-.5)*x = .5x        and  breadth=(1+.25)*y=1.25y

the area of the square (A')= .5x * 1.25y = .625 x*y

the perimeter of the square (P')=.5 *x*4 =2x

the ratio of the area of the rectangle and the square =1.6

the ratio of the perimeter of the rectangle and the square = x+y/x

∵ .5x=1.25 y

∴y = .4x

∴the ratio of the perimeter of the rectangle and the square  =1.4