The perimeters of square region s and rectangular region r are equal. if the sides of r are in the ratio 2 : 3, what is the ratio of the area of region r to the area of region s ?

The ratio of the area of region R to the area of region S is:

The sides of R are in the ratio : 2:3

Let the length of R be: 2x

and the width of R be: 3x

i.e. The perimeter of R is given by:

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:

)

Hence, we get:

i.e.

Also, let " s " denote the side of the square region.

We know that the perimeter of a square with side " s " is given by:

Now, it is given that:

The perimeters of square region S and rectangular region R are equal.

i.e.

Now, we know that the area of a square is given by:

and

Hence, we get:

and

i.e.

Hence,

Ratio of the area of region R to the area of region S is:

Answer with Step-by-step explanation:

the sides of rectangular region R are in the ratio 2 : 3.

i.e. If length=2x

then, breath=3x

Perimeter of rectangular region=2(length+breath)

                                    = 2(2x+3x)

                                    =10x

and Area of rectangular region=2x×3x

                                                  =length×breath

                                                  =6x²

Let s be the side length of square region S

Perimeter of square region=4s

The perimeters of square region S and rectangular region R are equal.

i.e. 4s=10x

s=

Area of square region=s²

                                    =

                                    =

Ratio of the area of region R to the area of region S

Hence, the ratio of the area of region R to the area of region S is:

24:25

tangent

step-by-step explanation: