Question

7. A portrait without its frame has

a height 1.5 times its width w, 131
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?
Simplify your expression and write
it in standard form.

Answer 1

1.5w² + 5w + 4

Explanation:

Answer 2

The standard form is A. 1.5w² + 5w + 4

Explanation:

Height of the portrait = 1.5 times its width in inches

Frame = 2 inches all along its perimeter

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