MNKP is a parallelogram. Find the length of the diagonal MK if the perimeter of the parallelogram

MNKP is a parallelogram. Find the length of the diagonal MK if the perimeter of the parallelogram is 62 cm and the perimeter of the triangle MNK is 44 cm.

1. The perimeter of the MNK triangle is calculated by the formula:

MN + NK + MK = 44 cm.

2. The sum of the sides of the parallelogram (perimeter):

МN + NК + КР + МР = 62 cm.Considering that the opposite sides of the parallelogram are equal,

this expression can be written like this:

2МN + 2NК = 62 cm.Divide this expression by 2:

MN + NK = 31 cm.

3. Substitute the value of this expression into the formula for calculating the perimeter of the triangle MNK:

31 + MK = 44 cm.

MK = 44 – 31 = 13 cm.

Answer: the length of the diagonal of the MK is 13 cm.