The rectangle is split into four smaller rectangles by two straight cuts. The perimeters of three of them

The rectangle is split into four smaller rectangles by two straight cuts. The perimeters of three of them, starting from the top left and further clockwise, are equal to 24, 28 and 16. Find the perimeter of the fourth rectangle.

The perimeter of the first rectangle is 24;

P = 2 * (a + b) = 24;

The perimeter of the second rectangle is 28;

P = 2 * (a + c) = 28;

The perimeter of the third rectangle is 16;

P = 2 * (d + c) = 16;

The perimeter of the fourth rectangle is:

P = 2 * (b + d).

Let us express the semi-perimeters of the quadrangles:

a + b = 12;

a + c = 14;

d + c = 8.

Let us express sides a and c:

a = 12 – b;

c = 14 – a.

Substitute expression a into the second equation:

c = 14 – 12 + b;

c = 2 + b.

Substitute this expression into the last equation:

d + 2 + b = 8;

d + b = 6.

This expression is the semiperimeter of the fourth rectangle.

P = 6 * 2 = 12.

Answer: 12.