Question

The surface area of each face of a cube is (x

2 + 6x + 9) m2

Find an expression for the,
i. length of each edge

Answer 1

length of each edge = (x + 3)

Explanation:

The surface area of each face of the cube = (
`x^(2)` + 6x + 9)
`m^(2)`. But the surface of a cube has the shape of a square. So that,

Area of a square = length x length

=
`l^(2)`

By factorizing the area,

`x^(2)` + 6x + 9 =
`x^(2)` + 3x + 3x + 9

= (
`x^(2)` + 3x) (3x + 9)

= x(x +3) + 3(x + 3)

= (x + 3)(x + 3)

=
`(x + 3)^(2)`

`x^(2)` + 6x + 9 =
`(x + 3)^(2)`

Thus,

`(x + 3)^(2)` =
`l^(2)`

find the square root of both sides

l = (x + 3)

length of each edge = (x + 3)