In the MNP parallelogram, the difference between the sides m n and n p is 2 cm, and the diagonal

In the MNP parallelogram, the difference between the sides m n and n p is 2 cm, and the diagonal is the height of the parallelogram. Find N Q if the perimeter of the parallelogram is 60cm.

Solution: since the perimeter is 60cm and is equal to 2 (mn + np), then mn + np = 30cm
mn-np = 2) system of equations, it can be solved by adding
mn + np = 30cm) term by term
2mn = 32, hence mn = 32/2 = 16, and np = mn-2 = 16-2 = 14
MN = PQ = 16cm and NP = MQ = 14cm
NQ is the diagonal and height of the parallelogram, and if it is the height of the triangle, MNQ is rectangular, in which NQ is the unknown leg
It can be found by the Pythagorean theorem: NQ = √MN ^ 2-NP ^ 2 = √16 ^ 2-14 ^ 2 = √112 = 2 √28
Answer: 2√28