# GED Math : Perimeter and Sides of Triangles

## Example Questions

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### Example Question #1 : Perimeter And Sides Of Triangles

If , then which segment is congruent to  ?

Explanation:

A congruency statement about two triangles implies nothing about the relationship between two sides of the same triangle, so we can eliminate . Also, the length of a segment with endpoints on two different  triangles depends on their positioning, not their congruence, so we can eliminate .

Since  and  are in the same positions in the name of the first triangle as  and  and  are corresponding sides of congruent triangles, and

Since the letters of the name of a segment are interchangeable, this statement can be rewritten as

,

making  the correct choice.

### Example Question #2 : Perimeter And Sides Of Triangles

A triangle has sides of length 36 inches, 3 feet, and one yard. Choose the statement that most accurately describes this triangle.

This triangle is equilateral.

This triangle is isosceles but not equilateral.

This triangle is scalene.

This triangle is equilateral.

Explanation:

One yard is equal to three feet, or thirty-six inches. The three given sidelengths are equal to one another, making this an equilateral triangle.

### Example Question #3 : Perimeter And Sides Of Triangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Explanation:

The altitude perpendicular to the hypotenuse of a right triangle divides that triangle into two smaller triangles similar to each other and the large triangle. Therefore, the sides are in proportion. The hypotenuse of the triangle is equal to

.

Therefore, we can set up a proportion and solve for :

### Example Question #4 : Perimeter And Sides Of Triangles

If the base of an equilateral triangle is 16cm, find the perimeter.

Explanation:

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

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 16cm. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 16cm.  So, we get

### Example Question #5 : Perimeter And Sides Of Triangles

The perimeter of an equilateral triangle is 36in.  Find the length of one side.

Explanation:

The formula to find the perimeter of an equilateral triangle is

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

Now, we know the perimeter of the equilateral triangle is 36in. So, we will substitute and solve for a. We get

Therefore, the length of one side of the equilateral triangle is 12in.

### Example Question #6 : Perimeter And Sides Of Triangles

Find the perimeter of an equilateral triangle with a side having a length of 17in.

Explanation:

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

where a, b, and c are the lengths of the sides of the triangle.

Now, we know one side of the triangle has a length of 17in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 17in. So, we can substitute. We get

### Example Question #7 : Perimeter And Sides Of Triangles

An equilateral triangle has a perimeter of 69in.  Find the length of one side.

Explanation:

The formula to find the perimeter of an equilateral triangle is

where a is the length of one 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, we will solve for a.

Now, we know the perimeter of the triangle is 69in. So, we can substitute and solve for a. We get

Therefore, the length of one side of the equilateral triangle is 23in.

### Example Question #8 : Perimeter And Sides Of Triangles

The perimeter of an equilateral triangle is 42cm.  Find the length of one side.

Explanation:

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

where a is the length of one side. An equilateral triangle has 3 equal sides, so we can use any side in the formula. To find the length of one side, we will solve for a. Now, we know the perimeter of the triangle is 42cm. So, we will substitute and solve for a. We get

Therefore, the length of one side of the equilateral triangle is 14cm.

### Example Question #9 : Perimeter And Sides Of Triangles

A triangle has the sides of , and .  What is the perimeter of the triangle?

Explanation:

The three sides of the triangle are known.  Add all the sides together.

### Example Question #10 : Perimeter And Sides Of Triangles

Suppose the perimeter of a triangle is . What must be the side length?

Explanation:

There are three sides in a triangle.

To determine the length of a side, multiply the quantity by one-third.