Let

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

b = the length of the base, h>0

A = 18 cm^2 the area

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

b = h + 5

The area is calculated by the formula: A = (1/2)b*h or

(1/2)bh = 39 multiply both sides by 2

bh = 78

plug b = h + 5 into the equation:

(h + 5)h = 78

........

click here to see the quadratic equation solved for h

........

h = 6.68 cm

6.68 + 5 = 11.68 cm

The height is 6.68 cm.

The length of the base is 11.68 cm.