let

a = the length of the base, a>0

h = the height of the triangle, h>0

A = 77 in^2 the area if the triangle

the base is 3 inches more than the height

a = 3 + h

h = a - 3

the area is calculated by the formula A = (1/2)a*h

(1/2)a*h = 77

plug h = a - 3 into the last equation

(1/2)a(a - 3) = 77

by solving we find

a = 14 in

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

the length of the base is 14 inches.