Question

each side of a rectangle is doubled find the ratio between i) perimeters of the original rectangle and resulting rectangle ii) area of the original rectangle and the resulting rectangle​

Answer 1

★ ANSWER :

1.The ratio between the original perimeter and the resulting perimeter of the rectangle is 1:2.

2. The ratio between the original area and resulting area of the rectangle is 1:4.

★ EXPLANATION :

•Given :-

• Each side of a rectangle is doubled.

•To find :-

Ratio between→

1. Perimeter of the original rectangle and resulting rectangle.
2. Area of the original rectangle and the resulting rectangle.

• Solution :-

✪CASE 1.

Let the length of the rectangle be x and the breadth of the rectangle be y.

We know,

Perimeter of rectangle, =2(length+breadth)

So, perimeter of original rectangle, =2(x+y)

ᴥ If length and breadth are doubled, then find the length and the breadth of the rectangle.

Length = 2x

Breadth= 2y

So, perimeter of resulting rectangle, =2(2x+2y)

= 4(x+y)

Original perimeter : Resulting perimeter

= 2(x+y) : 4(x+y)

= 1 : 2

Therefore, the ratio between the original perimeter and the resulting perimeter of the rectangle is 1:2.

✪CASE 2.

We know,

Area of rectangle,

=(length×breadth)

So, area of original rectangle,

= xy

ᴥ If length and breadth are doubled, then find the length and the breadth of the rectangle.

Length = 2x

Breadth= 2y

So, area of resulting rectangle,

= 2x × 2y

= 4xy

Original area : Resulting area

→xy : 4xy

→ 1 : 4

Therefore, the ratio between the original area and resulting area of the rectangle is 1:4.

Answer 2

Step-by-step explanation:

Given -

Each side of rectangle is doubled.

To Find -

• Ratio between perimeter of original rectangle and resulting rectangle.
• Ratio between area of original rectangle and resulting rectangle.

Now,

In the case of Original reactangle -

Let x be the length,

and y be the breadth of the rectangle.

Then,

Area of original rectangle = xy

And

Perimeter of original rectangle = 2(x + y)

And

In the case of Resulting rectangle -

Given -

Side of rectangle is doubled.

Then,

the length is 2x,

and breadth is 2y.

Then,

Area of resulting rectangle = 2x×2y = 4xy

And

Perimeter of resulting rectangle =

= 2(2x + 2y)

= 4x + 4y

= 4(x + y)

Now,

Ratio between perimeter of original rectangle and resulting rectangle is

2(x + y) : 4(x + y)

= 1 : 2

And

Ratio between area of original rectangle and resulting rectangle is

xy : 4xy

= 1 : 4

Hence,

Ratio between perimeter of original rectangle and resulting rectangle is 1 : 2

And

Ratio between area of original rectangle and resulting rectangle is 1 : 4