One of the diagonals of a parallelogram is its altitude. what is the length of this altitude, if its perimeter is 50cm, and the length of one side is 1cm longer than the length of the other? pls include full proof tysm

 A
   ]  
   |
   |
   D                                |  B
                                      |
                                      |
                                       C

Let ABCD be this parallelogram 
AB + BC + CD + DA = 50, but AD = BC  and AB = DC, Then:
2.AD + 2.AB = 50 and :
AD+AB = 25 . We also know that AB+1 = AD (Given), then:
AD + (AD+1) = 25
2.AD = 24 
AD = 12, THEN AB = 12+1=13
Calculate DB the diagonal perpendicular to AD, using Pythagoras:

AD² + DB² = AB²
12² +DB² = 13²
DB² = 13² - 12² = 25
AND DB= 5