### All ACT Math Resources

## Example Questions

### Example Question #1 : Equilateral Triangles

What is the perimeter of an equilateral triangle with an area of ?

**Possible Answers:**

**Correct answer:**

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of the small base to the height is the same as . Therefore, you can write the following equation:

This means that .

Now, the area of a triangle can be written:

, and based on our data, we can replace with . This gives you:

Now, let's write that a bit more simply:

Solve for . Begin by multiplying each side by :

Divide each side by :

Finally, take the square root of both sides. This gives you . Therefore, the perimeter is .

### Example Question #1 : Equilateral Triangles

An equilateral triangle with a perimeter of has sides with what length?

**Possible Answers:**

**Correct answer:**

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

### Example Question #1 : Equilateral Triangles

Jill has an equilateral triangular garden with a base of and one leg with a length of , what is the perimeter?

**Possible Answers:**

**Correct answer:**

Since the triangle is equilateral, the base and the legs are equal, so the first step is to set the two equations equal to each other. Start with , add to both sides giving you . Subtract from both sides, leaving . Finally divide both sides by , so you're left with . Plug back in for into either of the equations so that you get a side length of . To find the perimeter, multiply the side length , by , giving you .

### Example Question #2 : Equilateral Triangles

Find the perimeter of an equilateral triangle whose side length is

**Possible Answers:**

**Correct answer:**

To find perimeter of an quilateral triangle, simply multiply the side length by . Thus,

### Example Question #3 : Equilateral Triangles

Find the perimeter of an equilateral triangle whose side length is .

**Possible Answers:**

**Correct answer:**

To solve, simply multiply the side length by . Thus,

### Example Question #1 : Equilateral Triangles

Find the perimeter of an equilateral triangle given side length of 2.

**Possible Answers:**

**Correct answer:**

To solve, simply multiply the side length by 3 since they are all equal. Thus,

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