# SSAT Middle Level Math : How to find length of a line

## Example Questions

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### Example Question #216 : Geometry

Figure NOT drawn to scale.

Evaluate .

Explanation:

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

A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?

Explanation:

In geometry, a right angle triangle can occur with the ratio of  in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.

When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.

Here, the ratio is:

This is double the   ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.

Another way to solve is to use the Pythagorean Theorem: .

We know that one leg is 6 feet and the hypotenuse is 10 feet.

### Example Question #218 : Geometry

The radius of a circle is 6 inches. What is one-third of the diameter?

Explanation:

If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.

### Example Question #219 : Geometry

A right triangle has one leg with length  and another leg with length . What is the length of the hypotenuse?

Explanation:

Since we are dealing with a right triangle, we can use the Pythagorean Theorem:

,

where  and  are leg lengths of  and , respectively, and  is the length of the hypotenuse.

Substituting values into the Theorem:

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

Line  has a length of . It is bisected at point , and the resulting segment  is bisected again at point . What is the length of the line segment ?

Explanation:

A line that is bisected is split into two segments of equal length. Therefore, if line  is bisected at point

.

Consequently, bisecting line segment  at point :

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

Figure NOT drawn to scale.

Evaluate .

Explanation:

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

What is the length of a line segment with end points  and ?

Explanation:

The length of a line segment can be determined using the distance formula:

### Example Question #3 : How To Find Length Of A Line

What is the length of a line with endpoints and .

Explanation:

To find the length of this line, you can subtract to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

### Example Question #4 : How To Find Length Of A Line

Find the length of the line segment whose endpoints are and .

Explanation:

We can use the distance formula:

### Example Question #71 : Plane Geometry

The point lies on a circle. What is the length of the radius of the circle if the center is located at ?