SAT Math Multiple Choice Practice Question 170: Answer and Explanation

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Question: 170


In this figure, each side of the large center square is twice as long as each side of the four medium-sized squares. Each side of the medium-sized squares is twice as long as each side of the four small squares. If the small squares have sides of length 1 cm, find the perimeter of the entire figure.

A. 40 cm
B. 52 cm
C. 60 cm
D. 64 cm
E. 80 cm

Correct Answer: A


A. Because the small squares have side lengths of 1 cm, the medium squares' sides are 2 cm each, and the big square's sides are 4 cm each. Label the diagram as I do here:

The key is to count only the sides on the outside of the figure, which I conveniently darken in my drawing. Because the figure is symmetrical, focus on just one side. Here's the right side of the drawing:

Three little sides equal 3 cm. The medium square has two full sides and one half-side contributing to the perimeter, for 2 × 2 + 1 = 4 + 1 = 5 cm more. And the big square gives a half-side to the perimeter, for another 2 cm. Add them all together and you get 3 cm + 5 cm + 2 cm = 10 cm. Because the figure has four sides just like this one, the answer is 10 cm × 4 = 40 cm.

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