Write Triangles Named by the Lengths of Their Sides?

An equilateral triangle is a triangle with three congruent sides.

All three sides of this triangle are the same length.

An isosceles triangle is a triangle with two congruent sides.

Two of the sides of this triangle are the same length.

A scalene triangle is a triangle with no congruent sides.

All of the sides of this triangle have different lengths.

Applying Algebra to Side Lengths
Example 1: Find the length of one side of an equilateral triangle if the perimeter is 21. Find the length of one side of an equilateral triangle if the perimeter is 21.
Since all sides of an equilateral triangle are congruent, let x represent the length of each side.

X+ x+ x = 21 The perimeter can be represented by the following equation:

To find the length of the side, solve for x.
X+ x+ x = 21
3x= 21
3x/3=21/3
X=7
Example 2: Find the length of one of the congruent sides of an isosceles triangle if the third side is 10 and the perimeter is 48.
Let x represent the length of each congruent side.

The perimeter can be represented by the following equation:
X+x+10 =48
To find the length of one of the congruent sides, solve for x:
X+x+10 =48
2x+10 =48
-10 -10
2x = 38
2x/2 = 38/2
X= 19