All GRE Math Resources
Example Question #31 : Triangles
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 #32 : Triangles
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 .
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 #33 : Triangles
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 .
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.