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Problem 303

Geometry Difficulty 1.7 Multiple choice CEMC Gauss (Grade 7) · Canada · 2014

Sarah’s hand length is 20 cm. She measures the dimensions of her rectangular floor to be 18 by 22 hand lengths. Which of the following is the closest to the area of the floor?

Pick one

Official solution

The width of Sarah’s rectangular floor is 18 hand lengths.

Since each hand length is 20 cm, then the width of the floor is $18\times20=360$ cm.

The length of Sarah’s rectangular floor is 22 hand lengths.

Since each hand length is 20 cm, then the length of the floor is $22\times20=440$ cm.

Thus the area of the floor is $360\times440=158\,400$ cm $^2$ .
Of the given answers, the closest to the area of the floor is $160\,000$ cm $^2$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.