The side of the square is 10 inches.
The area of the square is thus
= side * side
= 10 * 10
= 100 inches^2
The square and triangle have the same area, so the area of the triangle is also 100 inches^2.
The formula for the area of a triangle is 1/2 * base * height.
Since the base of the triangle is 10 inches and its area is 100 inches^2, we have:
100 = 1/2 * 10 * height
100 = 5 * height
height = 100 / 5
height = 20 inches
Hence, the height of the triangle is 20 inches.