Answer:
Step-by-step explanation:
Let L represent the length of the original rectangle.
Let W represent the width of the original rectangle.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
The perimeter of a rectangle is 30 cm. This means that
2(L + W) = 30
Dividing through by 2,
L + W = 15
The area would be LW
If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. This means that
(L - 3)(W + 5) = LW - 8
LW + 5L - 3W - 15 = LW - 8
LW - LW + 5L - 3W = - 8 + 15
5L - 3W = 7 - - - - - - - - - - - 1
Substituting L = 15 - W into equation 1, it becomes
5(15 - W) - 3W = 7
75 - 5W - 3W = 7
- 5W - 3W = 7 - 75
- 8W = - 68
W = - 68/- 8 = 8.5
L = 15 - W = 15 - 8.5
L = 6.5
The area of the original rectangle is
6.5 × 8.5 = 55.25 cm²
