A portrait without its frame has a height 1.5 times its width w, in inches. Its frame is 2 in. wide all along its perimeter. What is an expression for the area of

the framed portrait in terms of w?

A. 1.5W2 + 5W + 4

B. 1.5w2 + 8w + 8

C. 1.5w2 + 8.5w + 16

D. 1.5w2 + 10w + 16

The correct answer is A. 1.5w² + 5w + 4

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the portrait = 1.5 times its width in inches

Frame = 2 inches all along its perimeter

2. What is an expression for the area of the framed portrait in terms of w?

Let's recall that the area of a rectangle is length or height * width.

A = height * width

Now, we can replace in terms of w:

A = 1.5w * w

But we need to add the 2 inches of the frame, this way:

A = (1.5w + 2) * (w + 2)

A = 1.5w² + 2w + 3w + 4

A = 1.5w² + 5w + 4

The correct answer is A. 1.5w² + 5w + 4