A square is cut into two congruent triangles by drawing the diagonal between two corners. If the area of each triangle is 162 cm, what is the length of the side of the square?

Ok so area=162

since the triangles sides were cut out of a square, base=height

area=1/2bh=162

b=h

area=1/2b^2=162

times 2 both sides

b^2=324

sqrt both sides

b=18=h

the legnth of one side is 18cm

see diagram

another way, is total aera of square=areas of both triangles=162+162=324

remember area of square=side^2 so

324=side^2

sqrt both sides

18=side

answer is 18cm