Answer:the original length of the rectangle is 50 m
the original width of the rectangle is 20 m
Explanation:
Let L represent the original length of the rectangle
Let W represent the original width of the rectangle.
The length of a rectangle is 10 m greater than twice its width. This means that
L = 2W + 10
Perimeter = 2(L + W)
= 2(2W + 10 + W) = 6W + 20
If the lengths were doubled and the widths were halved, the perimeter of the new rectangle would be 80 m more than the perimeter of the original rectangle. This means that
2(2L + W/2) = 6W + 20 + 80
4L + W = 6W + 100 - - - - - - - 1
Substituting L = 2W + 10, it becomes
4(2W + 10) + W = 6W + 100
8W + 40 + W = 6W + 100
8W + W - 6W = 100 - 40
3W = 60
W = 60/3 = 20
Substituting W = 20 into L = 2W + 10, it becomes
L = 2 × 20 + 10 = 50