Geometry: Quadrilaterals

Read the following SAT test question and then select your answer.

Remember the Knowsys Method: Without looking at the answer choices, read the question carefully, note the bottom line, assess your options, attack the problem, and loop back to check that you found what the question wanted.

What is the maximum number of nonoverlapping squares with sides of length 3 that will fit inside a square with sides of length 6?

At the top of your scratch work, summarize "the maximum number of nonoverlapping squares":

max squares = ?

Next, assess your options. There are two good ways to solve this quadrilaterals problem: visual and mathematical. Those who learn and think more visually can sketch or imagine a square with side length of 6, then reason that each side would be cut in half to make squares with sides of length 3. Two small squares touch each side of the large square, so four small squares total fit into the larger square.

Alternately, you can calculate the area of the large square and divide it among the smaller squares. The large square has sides of length 6, so its area is  . You will also need the area of the small squares. Their area is . Finally, divide the area of the large square by the area of the small square to determine how many will fit in the larger square.

Both methods gave 4. Now look at the answer choices:

A) Two
B) Three
C) Four
D) Six
E) Nine

The answer is C.

66% of responses on were correct.

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