15. What will happen to the area and perimeter of a rectangle if the
a. length and breadth are doubled?
b. length and breadth are reduced to half?
Answers
Answer. (1)area gets doubled if length is doubled while breadth remains same. ... so area increases by 4 times.
To Find:-
What will happen to the area and perimeter of a rectangle if :-
- Length and breadth are doubled
- Length and breadth are reduced to half.
Assumption:-
- Let the length and breadth of the original rectangle be l and b
Solution:-
For Area
For the original rectangle,
We know,
✭ Area of rectangle = (Length × Breadth) sq.un.
Hence,
Area of the original rectangle = l × b = lb
Now,
If the length and breadth are doubled
- Length = 2l
- Breadth = 2b
Area = 2l × 2b = 4lb
Let us divide the new area by original area,
= 4lb/lb = 4
∴ The area becomes 4 times if the length and breadth is doubled.
Now,
If the length and breadth are reduced to half
- Length = 1/2l
- Breadth = 1/2b
Area = 1/2l × 1/2b = 1/4lb
∴ The area become 1/4th of the original area of the length and breadth are reduced to half.
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For Perimeter
For original rectangle,
We know,
✭ Perimeter = 2(Length + Breadth) un.
Hence,
Perimeter = 2(l + b)
Now,
If the length and breadth are doubled,
- Length = 2l
- Breadth = 2b
Perimeter = 2(2l + 2b) units.
Let us divide the new perimeter of the new rectangle by the original one,
2(2l + 2b)/2(l + b)
⇒ (2l + 2b)/(l + b)
⇒ 2(l + b)/(l + b)
⇒ 2
∴ The perimeter becomes twice the original one if the length and breadth are doubled.
Now,
If the length and breadth are reduced to half,
- Length = 1/2l
- Breadth = 1/2b
Perimeter = 2(1/2l + 1/2b)
⇒ Perimeter = 2 × (l + b)/2
⇒ Perimeter = l + b
Let us divide the new perimeter by the original perimeter,
(l + b)/2(l + b) = 1/2
∴ The perimeter is reduced to 1/2 if the length and breadth are reduced to half.
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