In rectangle ABCD, the sum of sides AB and BC is 64 cm, and their difference is 4. Find the pyrometer and the area of the figure.

Consider rectangle ABCD.

By the condition of the problem, we have that:

AB + BC = 64,

AB – BC = 4.

Let’s add two equations:

(AB + BC) + (AB – BC) = 64 + 4,

2 * AB = 68,

AB = 34.

This implies that BC = 64 – AB = 64 – 34 = 30.

Thus, we have calculated the length and width of the given rectangle.

Therefore, we can calculate the perimeter P:

P = 2 * (AB + BC) = 2 * 64 = 128,

and the area S of the rectangle:

S = AB * BC = 34 * 30 = 1020.

Answer: The perimeter P of rectangle ABCD is 128 cm,

the area S is 1020 cm2.