The total area of a picture and its frame can be represented by ^l + 2f h^w + 2f h, where l and w represent the length and width of the picture, respectively, and f represents the thickness of the frame.

a. Sketch a diagram to represent this scenario.

b. What binomial multiplication represents the area of an 8" # 12" picture and its frame?

c. Multiply the binomials from b., and combine like terms to simplify.

d. What is the total area of an 8" # 12" picture and its frame if the frame is 1.5" thick?

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ogorwyne ogorwyne · Answer 1 · 2022-07-21T00:42:40+02:00

The answers to the question are

b. (l + 2f) (w + 2f)

c. f + 4, f + 6

d. 52.25

a. The diagram is an attachment.

The equation says

(l + 2f) (w + 2f)

We have the lengths of w and l as 8 and 12 respectively. Hence we have

(8 + 2f) (12 + 2f) as the area

c. (8 + 2f) (12 + 2f)

= 96 + 16f + 24f + 4f²

= 4f² + 40 f + 96

We have to factorize this using the quadratic equation calculator

f + 4, f + 6

= f = -4 and f = -6

d. If it is 1.25 thick we would have

1.25 x 2 = 2.5

12 - 2.5 = 9.5

8 - 2.5 = 5.5

Area = l * w

= 5.5 * 9.5

= 52.25

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