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 3/4 inches, and Frame B has a length of 7 1/2 inches.

Without calculating, predict which frame has the shorter width. Explain your reasoning

Answer 1

Frame B has the shorter width.

Explanation:

The area of a rectangle is given by length×width. If the two have a maintained area of 45 in², then length and width are inversely proportional, meaning if one goes up, the other must go down. Since Frame B has a larger length than Frame A and both frames have the same area, Frame B must have a shorter width to accommodate for its larger length.