### All Pre-Algebra Resources

## Example Questions

### Example Question #1 : Perimeter Of A Triangle

What is the area of a triangle with a base of units and a height of units?

**Possible Answers:**

**Correct answer:**

The equation for the area of a tirangle is

The base in this equation is and the height is which can be plugged into the formula as:

Finally, we multiply to get:

### Example Question #2 : Perimeter Of A Triangle

An equilateral triangle has one side with length . What is the perimeter of the triangle?

**Possible Answers:**

Not enough information is given.

**Correct answer:**

The key to solving this problem is remembering what an equilateral triangle is. In case you forgot, a quick word breakdown will help. It's easy to see that the first part of the word, "equi" looks an awful lot like equal. The second part, "lateral", is a little trickier, but we only need to remember that lateral means "side". In football, a lateral pass is when the player with the ball tosses it to a player on either side. Putting the two parts together, we see that equilateral just means equal sides. Therefore an equilateral triangle is a triangle where all three sides have equal length. That means that if one side of our equilateral triangle has length of , the other two sides are also each long.

We must also remember that the perimeter of a shape is just the distance around the outside of it. For our triangle, that means for the first side, for the second side, and for the third side. That means our perimeter is simply .

### Example Question #3 : Perimeter Of A Triangle

A right triangle has two short sides with lengths 5 and 12. What is the perimeter of the triangle?

**Possible Answers:**

25

36

32

30

28

**Correct answer:**

30

To begin, first find the length of the third side of the triangle. We are given that the two short sides of the triangle have lengths of 5 and 12. Use the Pythagorean Theorem to find the length of the third side:

,

where and represent the two shorter sides of the triangle, and is the hypotenuse:

Now that we have the lengths of all three sides, add them together to find the perimeter:

The perimeter of the triangle is 30.

### Example Question #4 : Perimeter Of A Triangle

Solve for the perimeter of the triangle.

Tom's, Bob's, and Fred's houses are in a triangle.

Tom's house is away from Bob's house. Fred's house is away from Bob's house. Fred's house is away from Tom's house.

What is the perimeter of the triangle between their houses?

**Possible Answers:**

**Correct answer:**

The correct answer to the question is .

The formula for finding the perimeter of a triangle is to find the sum of the length of the sides.

The lengths of the three sides of this triangle are , , and . If you add these sides, the sum is a perimeter of .

### Example Question #1 : Properties Of Triangles

What is the perimeter of a right triangle with hypotenuse and a leg of length ?

**Possible Answers:**

It cannot be determined from the information given.

**Correct answer:**

Using the Pythagorean Theorem, the length of the second leg can be determined.

We are given the length of the hypotenuse and one leg.

The perimeter of the triangle is the sum of the lengths of the sides.

### Example Question #5 : Perimeter Of A Triangle

Find the perimeter of the triangle above.

*Note: Figure not drawn to scale.*

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: .

Because the lengths are in inches, the answer must be in inches as well.

### Example Question #6 : Perimeter Of A Triangle

One side of an equilateral triangle is . What is the triangle's perimeter?

**Possible Answers:**

Not enough information given to solve.

**Correct answer:**

Equilateral triangles have sides of equal length. Therefore, by knowing the length of one side, we can calculate the perimeter by multiplying that length by .

### Example Question #7 : Perimeter Of A Triangle

In equilateral triangle , .

What is the perimeter of triangle ?

**Possible Answers:**

**Correct answer:**

Because the triangle is equilateral, all sidelengths are equal. Thus, if one is 8 they all must be 8, so

### Example Question #8 : Perimeter Of A Triangle

For an isosceles triangle, if two of the sides are 3 and 6, which of the following is a possible perimeter?

**Possible Answers:**

**Correct answer:**

In an isosceles triangle, two of the three sides are equal to each other. The possible side lengths of the isosceles are or .

The perimeter is the sum of the three sides.

The only possible perimeters given the two side lengths are either or .

The correct answer is:

### Example Question #9 : Perimeter Of A Triangle

What is the perimeter of an equilateral triangle with a length of 5?

**Possible Answers:**

**Correct answer:**

There are three equal sides in an equilateral triangle.

Substitute the side length.

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