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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #232 : Plane Geometry

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


I. 11

II. 15

III. 25

Possible Answers:

I Only

II Only

I and II Only

II and III Only

I, II and III

Correct answer:

II Only


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. 


  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.

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

Which of the following measurements can NOT represent the sides of a triangle. 

Possible Answers:

Correct answer:


Given the Triangle Inequality, the sum of any two sides of a triangle must be greater than the third side. 

Given the measurements :

Therefore, these lengths cannot represent a triangle. 

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