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27 May 2022, 03:14
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:22) correct
32%
(02:27)
wrong
based on 50
sessions
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Not Attempted Yet
A square photograph is set inside a square frame. If the photograph has a side length of n, and the width of the frame is p, which of the following represents the area of the frame?5
A. 2p^2 – n^2
B. 2(p^2 – n^2)
C. 2p(n + p)
D. 4p(n + p)
E. 4n(p^2 – n)
A. 2p^2 – n^2
B. 2(p^2 – n^2)
C. 2p(n + p)
D. 4p(n + p)
E. 4n(p^2 – n)
27 May 2022, 08:55
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Bunuel
We can do this one either by working with the variables or by plugging in. Let's do both.
Plugging In:
In the figure provided, the photo is 5x5 and the frame adds 2 inches to each side. We can see that the length of one side of the frame is going to be 5+2+2=9. The area of the whole thing is 9*9=81. The area of the photo is 5*5=25. So the area of the frame is 81-25=56. Let's check the answer choices.
(A) 2(4)-25 Wrong.
(B) 2(4-25) Wrong.
(C) 4(7)=28 Wrong.
(D) 8(7)=56 Keep it.
(E) 20(4-5) Wrong.
Answer choice D
Variables:
In the figure provided, the photo is n*n and the frame adds p inches to each side. We can see that the length of one side of the frame is going to be n+p+p=n+2p. The area of the whole thing is (n+2p)*(n+2p)=n^2+4np+4p^2. The area of the photo is n*n=n^2. So the area of the frame is n^2+4np+4p^2-n^2. Get rid of the n^2 and -n^2: 4np+4p^2. Factor out the 4p: 4p(n+p).
Answer choice D
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28 May 2022, 00:21
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Area of the frame = Area of the bigger square (whole figure) - Area of the photograph
= (p+n)^2 - n^2
= 4p^2 + n^2 + 4pn - n^2
= 4p^2 + 4pn
= 4p (n+p)
Hence, option D is the correct answer.
= (p+n)^2 - n^2
= 4p^2 + n^2 + 4pn - n^2
= 4p^2 + 4pn
= 4p (n+p)
Hence, option D is the correct answer.
