Respuesta :
Let Original rectangle has length L and Width W.
Perimeter = 18 inches
→2(L+W)=18
Dividing both sides by 2,we get
L+W=9 ........(1)
Now, new rectangle is formed by doubling the width Wand tripling the length L.
New length=3 L
New Breadth=2W
New perimeter=46 inches
→2(3 L+2W)=46
Dividing both sides by 2, we get
3L+ 2W=23
→L=9-W [Using 1]
Substituting in (2), we get
3(9-W)+2W=23
27-3W+W=23
W=27-23
W=4
and L=9-4=5 inches
So, Original rectangle has Length=5 inches, and Width=4 inches
The length of the formal rectangle = 5 inches
The width of the formal rectangle = 4 inches
The length of the new rectangle = 5 × 3 = 15 inches
The width of the new rectangle = 4 × 2 = 8 inches
perimeter of a rectangle = 2l + 2w
where
l = length
w = width
Therefore,
A rectangle having a perimeter of 18 inches can be represented as
- 2l + 2w = 18
- l + w = 9
The new rectangle formed will be
- 3(2l) + 2(2w) = 46
- 6l + 4w = 46
- 3l + 2w = 23
Combine the 2 equations
l + w = 9
3l + 2w = 23
l = 9 - w
3(9 - w) + 2w = 23
27 - 3w + 2w = 23
27 - w = 23
-w = 23 - 27
w = 4 inches
l + 4 = 9
l = 9 - 4
l = 5 inches
The length of the formal rectangle = 5 inches
The width of the formal rectangle = 4 inches
The length of the new rectangle = 5 × 3 = 15 inches
The width of the new rectangle = 4 × 2 = 8 inches
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