Question

Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 inches, and Frame B has a length of 7 inches. 1. Without calculating, predict which frame has the shorter width. Explain your reasoning. 2. Find the width that you predicted to be shorter. Show your reasoning.​

Answer 1

Frame B has the shorter width because it has a longer length and the area is the same for both frames. The width of Frame A is 7.5 inches, while the width of Frame B is approximately 6.43 inches.

Step-by-step explanation:

To predict which frame has the shorter width, we can examine the length and area of the frames. Frame A has a length of 6 inches and Frame B has a length of 7 inches. Since the area is the same for both frames and the width is inversely proportional to the length, we can conclude that Frame B, with a longer length, will have a shorter width.

To find the width, we can divide the area by the length. For Frame A, the width would be 45 square inches divided by 6 inches, giving us a width of 7.5 inches. For Frame B, the width would be 45 square inches divided by 7 inches, giving us a width of approximately 6.43 inches.

Answer 2

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Answer:

1. the longer frame (B) has the shorter width

2. the shorter width is 6 3/7 inches, area divided by length

Step-by-step explanation:

The relation between area, length, and width is ...

A = LW

Then the width is ...

W = A/L . . . . . inversely proportional to length

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1. Since length and width are inversely proportional (when area is constant), the shorter width will be associated with the longer length. Frame B will have the shorter width.

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2. The width of frame B is ...

W = A/L = (45 in²)/(7 in) = 45/7 in = 6 3/7 in