The two angles at bottom are marked as congruent. One forms a linear pair with a  angle, so it is supplementary to that angle, making its measure .  Therefore, each marked angle measures .

The sum of the measures of the interior angles of a triangle is , so:

A triangle must have at least two acute angles; however, a triangle with angles that measure  and  could have at most one acute angle, an impossible situation. Therefore, this triangle is nonexistent.

 ,

where  and   are the lengths of two sides and is the angle measure.

Plug in our given values:

 ,

where is the base and is the altitude.

The base can be seen as the (vertical) line segment connecting  and , which has length . The height is the pependicular distance from  to the segment; since the segment is part of the -axis, this altitude is horizontal and has length equal to -coordinate .

The area of this triangle is therefore

.

The base can be seen as the (horizontal) line segment connecting  and , the length of which is . The height is the pependicular distance from  to the segment; since the segment is part of the -axis, this altitude is vertical and has a length equal to -coordinate . 

The area of this triangle is therefore

.

The altitude of a right triangle from the vertex of its right angle - which, here, is  - divides the triangle into two triangles similar to each other as well as the large triangle.

The similarity ratio of  to  is the ratio of the lengths of their hypotenuses. The hypotenuse of the latter is 18; that of the former, from the Pythagorean Theorem, is

The similarity ratio is therefore . The ratio of their areas is the square of this, or 

The area of  is

of that of , so the choice closest to the correct percent is 25%.

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.