Question

if the perimeters of 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 for class 7 explains also​

Answer 1

Given :-

• Perimeter of rectangle = Perimeter of square

• The ratio of the two adjacent sides of rectangle is 1 : 2

Solution :-

According to the question,

Perimeter of rectangle = Perimeter of square

2( l + b) = 4 * side

Let the ratios be x and 2x and the side be S

Put the required values,

2 ( x + 2x ) = 4 * S

2 * 3x = 4s

6x = 4s

s = 6/4x

Now,

As we know that,

Area of rectangle = Length * Breath

Area of rectangle = x * 2x

Area of rectangle = 2x^2

As we know that,

Area of square = Side * Side

Area of square = 6/4x * 6/4x

Area of square = 36/16x^2 = 9/4x^2

Now,

We have to calculate ratio

Therefore,

Area of rectangle / Area of square

Put the required values,

= 2x^2 / 9/4x^2

= 8/9

Hence, The ratio of area of rectangle and square is 8:9 $.$

Answer 2

Step-by-step explanation:

Given :-

• Perimeter of rectangle = Perimeter of square

• The ratio of the two adjacent sides of rectangle is 1 : 2

Solution :-

According to the question,

Perimeter of rectangle = Perimeter of square

2( l + b) = 4 * side

Let the ratios be x and 2x and the side be S

Put the required values,

2 ( x + 2x ) = 4 * S

2 * 3x = 4s

6x = 4s

s = 6/4x

Now,

As we know that,

Area of rectangle = Length * Breath

Area of rectangle = x * 2x

Area of rectangle = 2x^2

As we know that,

Area of square = Side * Side

Area of square = 6/4x * 6/4x

Area of square = 36/16x^2 = 9/4x^2

Now,

We have to calculate ratio

Therefore,

Area of rectangle / Area of square

Put the required values,

= 2x^2 / 9/4x^2

= 8/9

Hence, The ratio of area of rectangle and square is 8:9 ..r

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