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
Answers
★ 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→
- Perimeter of the original rectangle and resulting rectangle.
- 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.
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