Geometry

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

First, read carefully and identify the bottom line. Make a note of the bottom line in your scratch work.Then consider the best way to solve the problem, asking "What could I do?" and "What should I do?" Select the fastest method and attack the problem. Finally, loop back to verify that you answered the question correctly.

The perimeter of a 7-sided figure is 15. If the length of each side of the figure is increased by 2 units, what is the perimeter of the new figure?

First, what is the bottom line? Mark it at the top of your scratch work using easy-to-understand shorthand:

new p=?

Next, ask "What could I do?" and "What should I do?" The problem gives the current perimeter and the number of sides, so you could determine the length of each side. You know how much each side changes, so you could calculate the total increase in perimeter. Now determine which one would be faster--if you divide to find the length of each side, you would then need to add the extra length and then multiply to find the total perimeter. If you find the increase in perimeter, you would only need to add that increase to the original perimeter to find the new distance around this polygon. This is the faster method, so attack!


You know that the polygon has 7 sides and that each side will increase in length by 2 units. 7*2=14, so the total perimeter will increase by 14 units. The original perimeter was 15, and 15+14=29, so the new perimeter is 29 units. Loop back to make sure that you answered what the problem was asking. new p was shorthand for the new perimeter, which is what you found, so now all you have to do is check the answer you found against the answer choices.

A) 17

B) 22

C) 24

D) 29

E) 30

The answer is D.

On sat.collegeboard.com, 71% of responses to this question were correct.


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