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

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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