Answer: original Length = 36 cm
Original width = 12 cm
Explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The length of a rectangle is three times the width. It means that
L = 3W
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
if the length is increased by 4 cm and the width is decreased by 1 cm the perimeter will be 102 cm. This means that
2[(L + 4) + (W - 1)] = 102
Dividing through by 2, it becomes
L + 4 + W - 1 = 51
L + W + 4 - 1 = 51
L + W + 3 = 51
L + W = 51 - 3
L + W = 48 - - - - - - - - - - - -1
Substituting L = 3W into equation 1, it becomes
3W + W = 48
4W = 48
W = 48/4
W = 12
L = 3W = 3 × 12
L = 36