All SSAT Middle Level Math Resources
Example Questions
Example Question #1 : Lines
Figure NOT drawn to scale.
Evaluate .
By the Segment Addition Postulate,
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?
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 #171 : Plane Geometry
The radius of a circle is 6 inches. What is one-third of the diameter?
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?
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
?
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 .
By the Segment Addition Postulate,
Example Question #2 : How To Find Length Of A Line
What is the length of a line segment with end points and
?
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
.
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
.
We can use the distance formula:
Example Question #1 : How To Find Length Of A Line
The point lies on a circle. What is the length of the radius of the circle if the center is located at
?
The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:
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All SSAT Middle Level Math Resources
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