Question

The perimeter of a rectangle is 30 cm. 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. Find the area of the original rectangle.

Answer 1

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