Painting problem?

Question

you own a painting whose dimensions are 24 by 30 inches. If you created a postcard size reproduction of the painting whose area is 20 square inches, what is the scaling factor for the reproduction?

A. 1/4 B 1/6 C 1/36 D 2/3

Answer 1

24" x 30" = 720 in²

20 in²/720 in² = 1/36

C
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MathBioMajor is totally correct. The scaling factor should be the factor by which you multiply the linear measurements, not the area measurements. The answer is √(1/36) = 1/6, answer B.

Answer 2

Jim Burnell is correct in that the ratio of the areas is 1/36. But then he forgot that this is a squared ratio, so he needed to have taken the square root of 1/36 to get the linear scaling factor.

The correct answer is B, 1/6. Here's why.

Suppose that the painting was a square in shape. Then its scaled version would be a square also, assuming each side was scaled equally. If we let the edge of the original painting be A = 12 (sq rt 5) inches in length, then its area is A² = 720 sq in. If we let the edge of the reproduction be B = 2 (sq rt 5) inches in length, then its area is B² = 20 square inches. I chose those particular lengths because when you square them, you get the correct area for each version of the painting.

Computing the ratio of their areas, we get this:

A²/B² = 720 / 20 = 36

A²/B² = 36 ---> B² / A² = (1/36) ---> B² = (1/36) A².

Taking the square root of both sides of the last equation, we get:

B = (1/6) A.

So the length of B is 1/6 of A, which implies 1/6 is the scaling factor.

To check, let's multiply each edge of the original painting by the scaling factor, then multiply those together to see what results.

24 (1/6) x 30 (1/6) = 4 x 5 = 20, which is the correct area. Notice that when you multiply 20 by 36, the square of the reciprocal of the scaling factor, you get 720, which is the area of the original painting.

Answer 3

lol are we doing your homework?

Answer 4

B....?