### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #1 : Plane Geometry

A triangle has sides feet, feet, and feet. Calculate its perimeter.

**Possible Answers:**

**Correct answer:**

The perimeter of any figure is the sum of the lengths of the sides: .

### Example Question #2 : Plane Geometry

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem, if and are the legs of a right triangle and is its hypotenuse, then

.

Set and solve for :

The perimeter of the triangle - the sum of the sidelengths - is

.

### Example Question #3 : Plane Geometry

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

**Possible Answers:**

**Correct answer:**

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

### Example Question #4 : Plane Geometry

Find the perimeter of a triangle with sides , , and .

**Possible Answers:**

**Correct answer:**

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals . Therefore, the answer is .

### Example Question #5 : Plane Geometry

A right triangle has legs feet and feet long. What is its perimeter, in inches?

**Possible Answers:**

**Correct answer:**

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute :

feet

Its perimeter is feet. Multiply by 12 to get the perimeter in inches:

inches

### Example Question #6 : Plane Geometry

An equilateral triangle has perimeter centimeters. How long is one side?

**Possible Answers:**

**Correct answer:**

An equilateral triangle has three sides of equal measure, so divide its perimeter by :

### Example Question #1 : Geometry

Find the perimeter of a right triangle, whose two legs are 5 and 12.

**Possible Answers:**

**Correct answer:**

To solve, you must first use the Pythagorean Theorem to solve for the hypotenuse and then add that value to the two perimeter values given.

Thus,

### Example Question #8 : Plane Geometry

If an equilateral triangle has a perimeter of , what is the length of one of its sides?

**Possible Answers:**

Cannot be determined

**Correct answer:**

An equilateral triangle has three equal length sides.

The perimeter of a triangle is all the sides added together.

Since all the sides are the same length the equation

is equal to

.

To find the side length, you just need to divide the perimeter by which is

.

### Example Question #9 : Plane Geometry

Find the perimeter of an equilateral triangle that has a side with a length of 11 inches.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a triangle, we use the following formula:

where *a, b, *and *c* are the sides of the triangle.

Now, we know the triangle is equilateral. This means that each side of the triangle is the same length. We know one side is 11 inches. Therefore, *all* sides are 11 inches. Knowing this, we can substitute. We get

### Example Question #10 : Plane Geometry

Find the perimeter of an equilateral triangle whose side measures 14 meters.

**Possible Answers:**

Cannot be determined from the information provided.

**Correct answer:**

Find the perimeter of an equilateral triangle whose side measures 14 meters.

The perimeter of a shape is simply the distance around it.

An equilateral triangle has three equal sides.

To find the perimeter in this case, simply multiply one side by 3.

So our answer is 42 meters.

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