Question

a museum sells postcards of famous paintings. the postcards must be the same shape as the painting. below are three options for the size of the postcard. a. which postcard could be the same shape as the painting? show your work.

Explanation:

Step1: Calculate the ratio of length to width for each postcard

For postcard A: The length and width are both 5 inches. The ratio of length to width is $\frac{5}{5}=1$.
For postcard B: The length is 8 inches and the width is 4 inches. The ratio of length to width is $\frac{8}{4} = 2$.
For postcard C: The length is 6.05 inches and the width is 5.05 inches. The ratio of length to width is $\frac{6.05}{5.05}=\frac{605\div5}{505\div5}=\frac{121}{101}\approx1.2$.

Step2: Determine the same - shape postcard

Since the postcards must be the same shape as the painting (assuming the painting has a square - like property if we consider the ratio for same - shape in terms of proportion of sides, and for a square the ratio of side to side is 1). Postcard A has a ratio of 1 (a square, all sides equal), while postcard B has a ratio of 2 (a rectangle with different side - length proportions) and postcard C has a non - 1 ratio.

Answer:

Postcard A could be the same shape as the painting.