If the length and width of a rectangle are doubled, what happens to the perimeter

Let's take a look at this problem.

Rectangle Perimeter = 2(l + w)

Rectangle Perimeter =? 2(2l + 2w)

Rectangle Perimeter =? (2)(2)(l + w)

2(Rectangle Perimeter) = 2[2(l + w)]

Thus, we can say that the perimeter of a rectangle is doubled when its dimensions are doubled.

Rectangle Area = lw

Rectangle Area =? (2l)(2w)

Rectangle Area =? 4lw

4(Rectangle Area) = 4lw

Thus, we can say that the area of a rectangle is quadruplicated when its dimensions are doubled.

If the length and breadth of a rectangle are doubled, how many times the perimeter of the old rectangle will that of the new rectangle be?

Let the length of the old rectangle = l
Let the breadth of the old rectangle = b
Perimeter of the old rectangle = 2(length + breadth) = 2(l + b)
When the length and the breadth of the rectangle are doubled, then
length of the new rectangle = 2l
breadth of the new rectangle = 2b
∴ Perimeter of new rectangle = 2(length + breadth)
= 2(2l + 2b)
= 2 × 2(l + b)
= 2 × perimeter of the old rectangle ..........[∵ perimeter of old rectangle = 2(l + b)]
Hence, the perimeter of the new rectangle will become two times the perimeter of the old rectangle.

Click here to see ALL problems on Rectangles Question 515421: If the length and width of a rectangle are doubled, how do the perimeters of the original and new rectangles compare? Found 2 solutions by richard1234, oberobic: Answer by richard1234(7193)     (Show Source): You can put this solution on YOUR website! The perimeter of the new rectangle is double. To show this algebraically, we let L and W be the length, width of the original rectangle. The perimeter is 2L + 2W. The new rectangle would have dimensions 2L and 2W, and the perimeter would be 2(2L ) + 2(2W) = 4L + 4W, or double the original perimeter. Answer by oberobic(2304)     (Show Source): You can put this solution on YOUR website! P = perimeter = 2(L+W) = 2L + 2W A = area = L*W . If you double L and W, you have 2L and 2W so P = 2(2L + 2W) = 4L + 4W which means the perimeter has doubled from 2L + 2W to 4L + 4W. . A = 2L*2W A = 4L*W . However, the area has quadrupled. Why? 2*2 = 4 . As a check, consider a rectangle with sides = 4 ft. (Yes, it's a square.) . P = 2(4+4) = 2(8) = 16 ft A = 4*4 = 16 sq ft . Now double the sides = 8 ft . P = 2(8+8) = 2*16 = 32 A = 8*8 = 64 . The perimeter doubled from 16 to 32 ft. The area quadrupled from 16 to 64. . Done.

If length and breadth of a rectangle are doubled then its perimeter too is doubled.

Explanation:

Perimeter of a rectangle whose length is #l# and breadth is #b# is

#2xx(l+b)#

If length and breadth are doubled, they become #2l# and #2b# and perimeter becomes

#2xx(2l+2b)=2xx2(l+b)=4(l+b)#

i.e. perimeter is doubled.

What happens to the perimeter of a rectangle if you double its length and width?

Does the perimeter of a rectangle double when both the length and the width are doubled?

How is the perimeter of a rectangle related to its length and width?

What happens to area of rectangle when the sides are doubled?