Math, asked by rssainidpr, 5 months ago

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?​


rssainidpr: and (b) solve plz

Answers

Answered by akirichinna
0

Answer. (1)area gets doubled if length is doubled while breadth remains same. ... so area increases by 4 times.

Answered by Anonymous
2

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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Anonymous: Perfect explanation
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