### All PSAT Math Resources

## Example Questions

### Example Question #1 : Acute / Obtuse Triangles

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 and III Only

I, II and III

II Only

I and II 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.

Jerry

Certified Tutor

Certified Tutor

North Carolina State University at Raleigh, Bachelor of Science, Applied Mathematics. Central Connecticut State University, M...

Stephanie

Certified Tutor

Certified Tutor

Saint Louis University-Main Campus, Bachelors, Psychology. University of Southern Mississippi, Masters, Clinical Psychology.