### All SAT 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, II and III

I Only

II and III Only

II Only

I and II Only

**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.

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.

### Example Question #141 : Geometry

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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