Question

the diagram shows a border that is 4 inches wide surrounding annies painting. write an expression, in factored form, that represents the area of the border. square inches

Explanation:

Step1: Calculate the area of the larger rectangle

The length of the larger rectangle is \(3x + 4+4=3x + 8\) inches and the width is \(12 + 4+4 = 20\) inches.
The area of a rectangle is \(A=\text{length}\times\text{width}\), so \(A_{1}=(3x + 8)\times20=60x+160\).

Step2: Calculate the area of the smaller rectangle

The area of the smaller rectangle (the painting) is \(A_{2}=3x\times12 = 36x\).

Step3: Calculate the area of the border

The area of the border \(A = A_{1}-A_{2}\).
\(A=(60x + 160)-36x\).
Simplify the expression: \(A=60x-36x + 160=24x+160\).
Factor out the greatest common factor. The GCF of \(24x\) and \(160\) is \(8\).
\(A = 8(3x + 20)\).

Answer:

\(8(3x + 20)\)