Question

Lauren is sewing a quilt using fabric squares.

The length of a side of a fabric square is represented by the expression x + 4.
Which expression represents the area of a fabric square?

4x + 6
2x + 8
x + 4
x2 + 8x + 16

Answer 1

x^2 + 8x + 16

Explanation:

Given length of square x + 4.

Area of square with side S is given by
`S^2`.

Therefore are of square with side x + 4 is given by
`(x + 4)^2`

Area of square =
`(x + 4)^2\\=>(x + 4)*(x + 4)\\=> x(x + 4) + 4(x + 4)\\=> x^2 + 4x + 4x + 4*4\\=> x^2 + 8x + 16`

Thus, x2 + 8x + 16 expression represents the area of a fabric square.