Answer:
length of each edge = (x + 3)
Step-by-step explanation:
The surface area of each face of the cube = ([tex]x^{2}[/tex] + 6x + 9) [tex]m^{2}[/tex]. But the surface of a cube has the shape of a square. So that,
Area of a square = length x length
= [tex]l^{2}[/tex]
By factorizing the area,
[tex]x^{2}[/tex] + 6x + 9 = [tex]x^{2}[/tex] + 3x + 3x + 9
= ([tex]x^{2}[/tex] + 3x) (3x + 9)
= x(x +3) + 3(x + 3)
= (x + 3)(x + 3)
= [tex](x + 3)^{2}[/tex]
[tex]x^{2}[/tex] + 6x + 9 = [tex](x + 3)^{2}[/tex]
Thus,
[tex](x + 3)^{2}[/tex] = [tex]l^{2}[/tex]
find the square root of both sides
l = (x + 3)
length of each edge = (x + 3)
