Question

The ratio of the area of the rectangle and square is 8:9. If the perimeter of each is 24 cm find the dimensions of the rectangle

Answer 1

Hey.

Here is the answer.

let side of square be a

so, perimeter = 4 a = 24 cm

so, side, a = 6 cm

So, area = a^2 = 6^2 = 36 cm^2 b

As, ratio of areas is 8 : 9

so, area of rectangle/ area of square = 8 / 9

or, area of rectangle / 36 = 8/9

or, area of rectangle = 8×36/9 =32 cm^2

so, l×b = 32

or, l = 32/b

As, 2( l + b) = 24______ perimeter

or, 2( 32/b + b ) = 24

or, 32 + b^2 = 12 b

or, b^2 - 12 b = 32

or, b^2 -12b + 36 = 32 + 36

or, ( b - 6)^2 = 68

or, b - 6 = 8.246

or, b = 2.246 cm

So, l = 32/2.246 = 14.247 cm

Thanks .