### All High School Math Resources

## Example Questions

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

Two similiar triangles have a ratio of perimeters of .

If the smaller triangle has sides of 3, 7, and 5, what is the perimeter of the larger triangle.

**Possible Answers:**

**Correct answer:**

Adding the sides gives a perimeter of 15 for the smaller triangle. Multipying by the given ratio of , yields 52.5.

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

Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?

**Possible Answers:**

0

The answer cannot be determined

30

15

10

**Correct answer:**

10

The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.

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

Two similiar triangles exist where the ratio of perimeters is 4:5 for the smaller to the larger triangle. If the larger triangle has sides of 6, 7, and 12 inches, what is the perimeter, in inches, of the smaller triangle?

**Possible Answers:**

25

18

20

23

**Correct answer:**

20

The larger triangle has a perimeter of 25 inches. Therefore, using a 4:5 ratio, the smaller triangle's perimeter will be 20 inches.

### Example Question #231 : 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

I, II and III

II Only

II and III 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 #1 : How To Find An Angle In An Acute / Obtuse Triangle

Solve for . (Not drawn to scale).

**Possible Answers:**

**Correct answer:**

The angles of a triangle must add to 180^{o}. In the triangle to the right, we know one angle and can find another using supplementary angles.

Now we only need to solve for .

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

If and , what is the measure of ?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

All of the interior angles of a triangle add up to .

If and , then

Therefore,

Now, will equal because and form a straight line. Therefore,

Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it .

### Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

**Possible Answers:**

**Correct answer:**

Interior angles of a triangle always add up to 180 degrees.

### Example Question #2 : Acute / Obtuse Triangles

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

**Possible Answers:**

**Correct answer:**

Since the sum of the angles of a triangle is , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

### Example Question #3 : Acute / Obtuse Triangles

Triangle ABC has angle measures as follows:

What is ?

**Possible Answers:**

19

79

44

90

57

**Correct answer:**

57

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation

After combining like terms and cancelling, we have

Thus

### Example Question #4 : Acute / Obtuse Triangles

The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?

**Possible Answers:**

**Correct answer:**

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and = the base angle

So the equation to solve becomes

Thus the vertex angle is 34 and the base angles are 73.