A triangle is cut from a rectangle. The height of the triangle is half the unknown side length s. The shaded area that is left is 84 sq inches. What is the length of s.

so we know that the area of the triangle is the height multiplied by its base and divided by 2, here we have s as base, and height as s/2, so we have: area = base*height/2 = s(s/2)(1/2) = s^2/4 = 84 s^2 = 4*84 = 336 s = 18.33 that is the s side length 18.33 in^2