Question

The ratio between the sides of two square is2:5. Find the ratio between the (a) perimeters (b)areas​

Answer 1

Answer:

The ratio between the (a) perimeters  is 2:5 and (b)areas​ is 4:25.

Step-by-step explanation:

The ratio between the sides of two square is2:5.

Let us consider the side of the two square be $2x$ and $5x$ Respectively.

We know that,

        Perimeter of a square =$4 \cdot side$

So the perimeter of the first square =$4\cdot 2x=8x$

The perimeter of the second square =$4 \cdot 5x=20x$

Ratio of perimeter of the two square =$\frac{8x}{20x} =\frac{2}{5}$

We know that,

Area of the square =$(side)^2$

Area of the first square =$(2x)^2=4x^2$

Area of the second square =$(5x)^2=25x^2$

Ratio between area of the two square =$\frac{4x^2}{25x^2} =\frac{4}{25}$

Answer 2

Answer:

a) Ratio of perimeters of square 1 to square 2 $=2:5$

b) Ratio of areas of square 1 to square 2 $=4:25$

Step-by-step explanation:

Given the ratio between the sided of two squares as $2:5$ .

That is if side of square-1 $=2x$ ,

then side of square-2 $=5x$ .

Therefore,

a) Perimeter of a square of side $a\ cm$ $=4a$

   Thus the perimeter of the square of side $2x\ cm$ $=4*2x=8x$

   and the perimeter of the square of side $5x\ cm$ $=4*5x=20x$ .

Therefore the ratio of perimeters of square 1 to square 2 $=8:20=2:5$

(same as ratio of side)

b) Area of a square with side $a\ cm$ $=$ $a^{2}\ cm^{2}$ .

    Thus the area of the square with side $2x\ cm$ $=(2x)^{2} = 4x^{2}\ cm^{2}$

     and the area of the square with side $5x\ cm=(5x)^{2} =25x^{2} cm^{2}$

Therefore the ratio of areas of square 1 to square 2 is $4:25$ .

Hence the answer.

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