let

h = the height of the triangle

a = the length of the base

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

a = h + 7

the area is 22cm^2

(1/2)a*h = 22

plug a = h + 7 into the last equations

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

by solving we find and consider the positive roots since the height can not be a negative number

h = 4 cm

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a = h + 7

a = 4 + 7

a = 11 cm

the height is 4 cm.

the base is 11 cm.