The side of the rectangle, the length of which is 24 cm, was reduced by 8 cm and received a rectangle

The side of the rectangle, the length of which is 24 cm, was reduced by 8 cm and received a rectangle, the area of which is 96 cm2 less than the area of this rectangle. Find the area of the given rectangle and the perimeter of the new rectangle.

One rectangle has measurements: 24 cm – length, G cm – width, 24 * G cm2 – its area.

The new rectangle has dimensions: 24 – 8 = 16 cm – length, G cm – width, 16 * G cm2 – its area. Its area is less than the area of ​​the first by 96 cm2.

Equations: 24 * G – 16 * G = 96 (either 24 * G = 16 * G + 96; or 24 * G – 96 = 16 * G).

8 * G = 96.

G = 12.

24 * 12 = 288 cm2 – the area of ​​the 1st rectangle.

16 * 2 + 12 * 2 = 56 cm – the perimeter of the new rectangle.

Method 2 (arithmetic).

You can place one rectangle on top of another, aligning the width, then the “extra” rectangle will have an area of ​​96 cm, and its length – 8 cm, then 96: 8 = 12 cm is the width of each of the three rectangles.

24 * 12 = 288 cm2 – the area of ​​the 1st rectangle.

(16 + 12) * 2 = 56 cm – the perimeter of the new rectangle.