All GRE Math Resources
Example Questions
Example Question #4 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle
What is a possible value for the length of the missing side?
For a triangle where the length of two sides, and , is the only information known, the third side, , is limited in the following matter:
For the triangle given:
.
Both choices A and B satisfy this criteria.
Example Question #3 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle
A triangle has sides of lengths and
Quantity A: The length of the missing side.
Quantity B:
The relationship cannot be determined.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than .
Quantity A is greater.
Example Question #82 : Geometry
The lengths of two sides of a triangle are and .
Quantity A: The length of the missing side.
Quantity B:
Quantity B is greater.
The relationship cannot be determined.
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined.
Seeing the sides and may bring to mind a triangle. However, we've been told nothing about the angles of the triangle. It could be right, or it could be obtuse or acute.
Since the angles are unknown, the side is bounded as follows:
There are plenty of potential lengths that fall above and below . The relationship cannot be determined.
Example Question #83 : Geometry
A triangle has sides and
Quantity A: The length of the missing side.
Quantity B:
The relationship cannot be determined.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides and , there is no way a side could be .
Quantity B is greater.
Example Question #1 : How To Find The Perimeter Of An Equilateral Triangle
Find the perimeter of an equilateral triangle with a height of .
None of the answer choices are correct.
Perimeter is found by adding up all sides of the triangle. All sides in an equilateral triangle are equal, so we need to find the value of just one side to know the values of all sides.
The height of an equilateral triangle divides it into two equal 30:60:90 triangles, which will have side ratios of 1:2:√3. The height here is the √3 ratio, which in this case is equivalent to 8, so to get the length of the other two sides, we put 8 over √3 (8/√3) and 2 * 8/√3 = 16/√3, which is the hypotenuse of our 30:60:90 triangle.
The perimeter is then 3 * 16/√3, or 48/√3.
Example Question #2 : How To Find The Perimeter Of An Equilateral Triangle
If the height of an equilateral triangle is , what is the perimeter?
By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.
The height is opposite the angle . We can set-up a proportion.
Side opposite is and the side of equilateral triangle which is opposite is .
Cross multiply.
Divide both sides by
Multiply top and bottom by to get rid of the radical.
Since each side is the same and there are three sides, we just multply the answer by three to get .
Example Question #2 : How To Find The Perimeter Of An Equilateral Triangle
If area of equilateral triangle is , what is the perimeter?
The area of an equilateral triangle is .
So let's set-up an equation to solve for .
Cross multiply.
The cancels out and we get .
Then take square root on both sides and we get . Since we have three equal sides, we just multply by three to get as the final answer.
Example Question #1 : Equilateral Triangles
What is the length of a side of an equilateral triangle if the area is ?
The area of an equilateral triangle is .
So let's set-up an equation to solve for .
Cross multiply.
The cancels out and we get .
Then take square root on both sides and we get as the final answer.
Example Question #83 : Geometry
If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?
By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.
The height is opposite the angle . We can set-up a proportion.
Side opposite is and the side of equilateral triangle which is opposite is .
Cross multiply.
Divide both sides by
Multiply top and bottom by to get rid of the radical.
Example Question #81 : Geometry
What is the area of an equilateral triangle with a base of ?
An equilateral triangle can be considered to be 2 identical 30-60-90 triangles, giving the triangle a height of . From there, use the formula for the area of a triangle: