A scalene triangle, by definition, has three sides of different lengths. We can identify the scalene triangle by converting measures to the same unit. We will convert to inches in this case.

5 feet =  inches. This triangle can be eliminated, since two sides have length 60 inches.

7 feet =  inches. This triangle can be eliminated, since two sides have length 84 inches.

These three measures are equal. This is an equilateral triangle, and it can be eliminated.

 feet =  inches. This triangle can be eliminated, since two sides have length 66 inches.

5 feet = 60 inches. 

6 feet =  inches.

The sides of this triangle measure 60, 72, and 84 inches, so the triangle is scalene.

First you need to recognize that for an equilateral triangle, all 3 sides have equal lengths.

This means you can set the two values for Side A and Side B equal to one another, since they measure the same length, to solve for .

You now know that , but this is not your answer. The question asked for the length of Side A, so you need to plug 3 into that equation.

So the length of Side A (and Side B for that matter) is 8.

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°.  Since all sides are congruent, the other two sides both measure 12 centimeters.

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of any side of the triangle.  Because an equilateral triangle has 3 equal sides, we can use any side in the formula.  To find the length of one side of the triangle, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 18in.  So, we will substitute.

Therefore, the length of one side of the equilateral triangle is 6in.

An equilateral triangle has 3 equal sides.  So, to find the length of one side, we will use what we know.  We know the perimeter of the equilateral triangle is 39in.  So, we will look at the formula for perimeter.  We get

where a is the length of one side of the triangle.  So, to find the length of one side, we will solve for a.  Now, as stated before, we know the perimeter of the triangle is 39in.  So, we will substitute and solve for a.  We get

Therefore, the length of one side of the equilateral triangle is 13in.

An equilateral triangle with perimeter  has three congruent sides of length

The area of this triangle is 

, so

An equilateral triangle with perimeter  has three congruent sides of length

The area of this triangle is 

An equilateral triangle with perimeter  has three congruent sides of length . Substitute this for  in the following area formula:

The trick is to know that the circumscribed circle, or the circumcircle, has as its center the intersection of the three altitudes of the triangle, and that this center, or circumcenter, divides each altitude into two segments, one twice the length of the other - the longer one being a radius. Because of this, we can construct the following:

Each of the six smaller triangles is a 30-60-90 triangle, and all six are congruent.

We will find the area of , and multiply it by 6.

By the 30-60-90 Theorem, , so the area of  is

.

Six times this -  - is the area of .