Question

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

Answer 1

The expression for the area of the framed portrait in terms of w is 1.5w^2 + 8w + 8.

Step-by-step explanation:

To find the expression for the area of the framed portrait, we need to consider the dimensions of both the portrait and the frame. Let's assume the width of the portrait is w inches. According to the given information, the height of the portrait without the frame is 1.5 times the width, so the height is 1.5w inches.

To calculate the dimensions of the framed portrait, we need to add 2 inches to the width and height for the frame. The width of the framed portrait is w + 2 inches, and the height is 1.5w + 2 inches.

The area of the framed portrait is equal to the product of its width and height. Therefore, the expression for the area, in terms of w, is (w + 2) * (1.5w + 2). When we simplify this expression, we get 1.5w2 + 8w + 8.

Answer 2

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