Answer:
15 inches
Step-by-step explanation:
We assume that the edge of the small square is x (inches).
As the edge of the larger square is 2 inches greater than that of the smaller one, so that the edge of the larger square = edge of the small square + 2 = x + 2 (inches)
The equation to calculate the are of a square is: Area = Edge^2
So that:
+) The area of the larger square is: Area large square = [tex](x+2)^{2}[/tex] (square inches)
+) The area of the smaller square is: Area small square = [tex]x^{2}[/tex](square inches)
As difference in area of both squares are 64 square inches, so that we have:
Area large square - Area small square = 64 (square inches)
=> [tex](x+2)^{2} -x^{2} =64[/tex]
=> [tex]x^{2}+4x+4 -x^{2} =64[/tex]
=> 4x + 4 = 64
=> 4x = 64 - 4 = 60
=> x = 60/4 = 15 (inches)
So the length of an edge of the smaller square is 15 inches
