### All ISEE Lower Level Math Resources

## Example Questions

### Example Question #371 : Plane Geometry

Find the length of one side of an equilateral triangle that has a perimeter of 27cm.

**Possible Answers:**

**Correct answer:**

The formula to find perimeter of an equilateral triangle is

where *a* is the length of one side. We can multiply that by 3, because an equilateral triangle has 3 equal sides. Now, to find the length of one side, we will solve for *a*.

So, we know the perimeter of the equilateral triangle is 27cm. Knowing this, we can substitute. We get

Therefore, the length of one side of the equilateral triangle is 9cm.

### Example Question #391 : Geometry

Use the following triangle to answer the question:

Find the perimeter.

**Possible Answers:**

**Correct answer:**

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

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

Now, given the triangle

we can see that it has sides of length 8ft, 4ft, and 7ft. So, we get

### Example Question #371 : Plane Geometry

An equilateral triangle has a perimeter of 42 cm. What is the length of one of its sides?

**Possible Answers:**

**Correct answer:**

By definition, an equilateral triangle is a triangle with three equal sides. That is, the length of each side of the triangle is going to be the same.

In this problem, we know that the perimeter (the sum of all the lengths) is 42 cm.

Side 1 + Side 2 + Side 3 = 42 cm.

Since the sides are equal, we can write the following equation. one side of the triangle

To find the length of one side of the triangle, we would then divide 3 from both sides.

Remember that is the same as

### Example Question #1 : How To Find Symmetry

There is a four sided figure in which none of the lines run parallel to each other. Which of the following could be the appropriate term to describe the figure?

**Possible Answers:**

Parallelogram

Trapezoid

Rectangle

Quadrilateral

None of these

**Correct answer:**

Quadrilateral

A key characteristic of a rectangle, parallelogram, and trapezoid is the fact that they each have at least one pair of lines that run parallel to each other. The only option that has lines that may *not *run parallel to each other is the quadrilateral, which must simply have four sides but has no specifications about parallelism.

### Example Question #1 : Lines

If a diagonal is drawn from one corner of a rectangle to the opposite corner, what 2 shapes result?

**Possible Answers:**

**Correct answer:**

While drawing a line across a rectangle (so that it bisects 2 sides) can result in 2 quadrilaterals, squares, or rectangles, a line drawn from one corner to the furthest corner results in two triangles. Therefore, the correct answer choice is 2 triangles.

### Example Question #3 : How To Find Symmetry

How many lines of symmetry are there in a square?

**Possible Answers:**

**Correct answer:**

A line of symmetry is a line that divides a polygon in half and each half is a mirror image of the other. In other words, you can fold the polygon over the symmetry line and each half matches up perfectly.

For a square there are four lines of symmetry. Two are from the diagonals of the square and two are from connecting the midpoints of the opposite sides.

### Example Question #1 : How To Find Length Of A Line

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is .

Let and :

### Example Question #2 : Lines

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is given by .

Let and :

### Example Question #2 : How To Find Length Of A Line

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is given by .

Let and :

### Example Question #372 : Plane Geometry

What is the distance between the points and ?

**Possible Answers:**

**Correct answer:**

The distance formula is .

Let and .

Plug these two points into the distance formula: