What are the length and width of the picture without the frame? Select a width and length below.

Question

A framed picture has a total area y, in square inches. The thickness of the frame is represented by x, in inches. The equation y = (8 + 2x) (10 + 2x) relates these two variables.

What are the length and width of the picture without the frame? Select a width and length below.

Select choices seen below:

a. 4 inches

b. 8 inches

c. 10 inches

d. 5 inches

Answer 1

8 and 10. In the formula x is the thickness of the frame and (8+2x)(10+2x) = the area of the picture plus frame. If there is no frame then x=0. Then 8+2(0) = 8 and 10+2(0) = 10

Answer 2

The total area of the picture is y = (8+2x)(10+2x) , Expand

y = 80 + 16x + 20x + 4x² , simplify y = 4x² + 36 x + 80 is the area of the picture including the frame

Since x is the width of the frame, then the area of the picture excluding the frame is y when x = 0

y = 80, The combination of length and width that will give 80 is L = 10 inch, and W= 8 in

You can also use the original equation of the area y = (8+2x)(10+2x) and set x =0, y =80

from the above choices it is b. for the width and c. for the length