The diagonal of the quadrilateral is 10 cm, and the perimeter of one of the triangle into which this diagonal

The diagonal of the quadrilateral is 10 cm, and the perimeter of one of the triangle into which this diagonal splits this quadrilateral is 40 cm, find the perimeter of the other triangle if the perimeter of the quadrilateral is 53 cm.

1. Let a, b, c, d be the lengths of the sides of the original quadrilateral.
It is known that its perimeter is 53 cm.
P = a + b + c + d = 53.
2. Let k be the length of the diagonal.
Let’s write down the perimeters of the resulting triangles.
P1 = a + b + k.
P2 = c + d + k.
3. Add the perimeters of the two triangles.
P1 + P2 = a + b + k + c + d + k.
Now let’s regroup and replace all known values with numbers.
P1 + P2 = (a + b + c + d) + 2 * k.
40 + P2 = 53 + 2 * 10.
P2 = 53 + 20 – 40.
P2 = 33 cm.
Answer: the perimeter of the second triangle is 33 cm