The perimeter of the quadrilateral is 44 dm. The line connecting two opposite vertices divides it into two triangles

The perimeter of the quadrilateral is 44 dm. The line connecting two opposite vertices divides it into two triangles, the perimeter of which is 34 and 26 dm. Find the length of this line.

Let the sides of the quadrangle be a, b, c, d.

The length of the line connecting two opposite lines of the quadrilateral is X.

Let’s write the equations for the perimeter of the quadrangle:

P = a + b + c + d = 44 dm.

Perimeter of the first triangle:

P1 = a + d + X = 34 dm.

Perimeter of the second triangle:

P2 = b + c + X = 26 dm.

Let us add the equations and values of P1 and P2:

a + d + X + b + c + X = 34 + 26 = 60.

(a + b + c + d) + 2 * X = 60.

2 * X = 60 – 44 = 16.

X = 8 (dm).

Answer: the length of the required line is 8 dm.