Let x = the base
Let y = the height
Set up equations to represent the sum and the area.
x + y = 15 eq1
xy / 2 = 28
xy = 56 eq2
We need to find two numbers that give a sum of 15 at the same time, give a product of 56.
Two numbers that satisfy both conditions are 7 and 8. This is because when you add them, you get 15. When you multiply them, you get 56.
Therefore the base and height is 7 cm and 8 cm. The order does not matter at all.