The diagonal divides a rectangle with a perimeter of 31 cm into 2 triangles with perimeters of 21 cm

The diagonal divides a rectangle with a perimeter of 31 cm into 2 triangles with perimeters of 21 cm and 30 cm. The length of this diagonal is.

1. Let’s denote the four sides of the quadrangle by a, b, c, d, the diagonal by x; the perimeter of the quadrangle is behind P1, the perimeter of one triangle is behind P2, the perimeter of the second triangle is behind P3.

2. Let us write down the system of equations, to which the perimeters Р1, Р2, Р3 are equal in literal expression.

a) Р1 = a + b + c + d = 31 cm.

b) P2 = a + b + x = 21 cm.

c) P3 = c + d + x = 30 cm.

3. Let us add the equation b) and c);

P2 + P3 = a + b + x + c + d + x = 51cm;

From equation a) we substitute the sum of the sides a + b + c + d = 31 cm

and get

31 cm + 2 x = 51 cm;

2 x = 51 cm – 31 cm = 20 cm;

x = 10 cm.

Answer: The diagonal of the quadrangle is 10 centimeters.