Question

Christa has a picture frame that measures x in by (x + 2) in. The picture opening measures (x - 1)in by (x + 1)in. Write an equation, A(x), for the area of the picture frame, not including the opening.

Answer 1

A(x) = 2x - 1

Explanation:

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Answer 2

Explanation:

Area of rectangles

The area of a rectangle of dimensions x and y is

`A=xy`

The picture frame measures x and x-2 inches. The picture opening measures (x - 1) by (x + 1) inches. The external area of the frame is

`A_e=(x)(x-2)=x^2-2x`

The area of the picture opening is

`A_o=(x-1)(x+1)=x^2-1`

The ares of the frame, not including the picture opening is the difference

`A(x)=A_e-A_o=x^2-2x-(x^2-1)=-2x+1`

`A(x)=-2x+1\ inches`