SAT Math Multiple Choice Practice Question 7: Answer and Explanation

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Question: 7

7. In a triangle, the second side is 3 cm longer than the first side. The length of the third side is 5 cm less than twice the length of the first side. If the perimeter is 34 cm, find the length, in centimeters, of the longest side.

A. 3
B. 8
C. 9
D. 12
E. 13

Correct Answer: E


E. Quick quiz: What's the first thing you need to do when you read this problem? If you answered, "Draw the triangle," you win a prize! (The prize, of course, is an improved SAT score.) Drawing the triangle is only half the battle, though; you also have to label the triangle properly. Here you can use a guideline developed by a former colleague of mine: Let your variable stand for the second thing mentioned in the problem. In this case, the second thing mentioned is the first side, so let x = the first side. The second side is then x + 3, and the third side is 2x - 5. (Don't fall into the trap of thinking it's 5 - 2x.) The finished triangle looks like this:

The perimeter, 34, is the sum of all the sides, so (x) + (x + 3) + (2x - 5) = 34. Combining the like terms on the left side gives you 4x - 2 = 34. Adding two to each side gives you 4x = 36, which leaves you with x = 9. Now you need to plug 9 into the original equations: The first side is 9 cm, the second is 9 + 3 = 12 cm, and the third is 2(9) - 5 = 13 cm. Because this third side is the longest, 13 cm is the answer.

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