let

b = the length of the base of the triangle, b>0

h = the height of the triangle, h>0

The base of a triangle is 7cm greater than the height

b = 7 + h

The area is 22cm:

(1/2)bh = 22

plug b = 7 + h into the last equation:

(1/2)(7 + h)h = 22

by solving we find:

h = 4 cm

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l = 7 + 4

l = 11 cm

the height is 4 cm.

the length of the base is 11 cm.