The perimeter of the polygon is 76 cm. It is divided by the diagonals D into two polygons

The perimeter of the polygon is 76 cm. It is divided by the diagonals D into two polygons with perimeters of 67 cm and 49 cm. Diagonal length D?

1. Let’s denote one part of the perimeter of the original rectangle, which is obtained after splitting P1. This perimeter is equal to the difference between the perimeter of one of the two polygons and the diagonal obtained after splitting. Let’s write down what this perimeter is equal to:

P1 = 67 – D.

2. Let’s denote the second part of the perimeter P2. Let’s write down what this perimeter is equal to:

P2 = 49 – D.

3. The entire perimeter of the original rectangle is 76 cm. Let’s write the expression:

P1 + P2 = 76.

4. Substitute P1 and P2 into the resulting expression and solve the resulting equation:

(67 – D) + (49 – D) = 76;

67 – D + 49 – D = 76;

116 – 2D = 76;

2D = 40;

D = 40/2;

D = 20 (cm).

Answer: the length of the diagonal is 20 cm.