PSAT Math : How to find the perimeter of an acute / obtuse triangle

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

If a = 7 and b = 4, which of the following could be the perimeter of the triangle?

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I. 11

II. 15

III. 25

Possible Answers:

I, II and III

II and III Only

II Only

I and II Only

I Only

Correct answer:

II Only

Explanation:

Consider the perimeter of a triangle:

  P = a + b + c

Since we know a and b, we can find c. 

In I:

  11 = 7 + 4 + c

  11 = 11 + c 

  c = 0

Note that if c = 0, the shape is no longer a trial. Thus, we can eliminate I.

In II:

  15 = 7 + 4 + c

  15 = 11 + c

   c = 4.

This is plausible given that the other sides are 7 and 4. 

In III:

  25 = 7 + 4 + c

  25 = 11 + c

  c = 14.

It is not possible for one side of a triangle to be greater than the sum of both of the other sides, so eliminate III. 

Thus we are left with only II.

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