let

h = the the length of the height, a>0

a = the length of the base, h>0

A = 18 cm^2 the area

the base of a triangle is 5 cm greater than the height

a = h + 5

the are A = (1/2)a*h

(1/2)a*h = 18

plug a = h + 5 into the last equation

(1/2)(h + 5)h = 18

by solving we find

h = 4 cm

click here to see the step by step solution of the equation

a = 4 + 5

a = 9 cm

the height is 4 cm.

the length of the base is 9 cm.