Question

A portrait without its frame has a height of 2.5 times its width w, in inches. It's frame is 2 in. Wide all along it's perimeter. What is an expression for the area of the frame portrait and in terms of a.

Answer 1

Answer:

$Area, a=2.5w^2+14w+16$

Step-by-step explanation:

Without the Frame

The width of the portrait  =w

Height of the Portrait = 2.5w

Since the frame is on opposite sides of each dimension, it is added twice.

The width of the portrait with frame = w+2+2=4+w

Height of the Portrait with frame = 2.5w+2+2=4+2.5w

We are to write an expression for the area, a of the frame in terms of w (I presume)

Area= Width X Height

a=(4+w)(4+2.5w)

$a=4(4+2.5w)+w(4+2.5w)\\=16+10w+4w+2.5w^2\\a=2.5w^2+14w+16$