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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Perimeter And Sides Of Triangles

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Possible Answers:

$x = 10 \frac{12}{13}$

$X = 11\frac{1}{13}$

x = 10

$X= 10 \frac{1}{12}$

Correct answer:

$X = 11\frac{1}{13}$

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

$\sqrt{5^{2}+12^{2}} = \sqrt{25+144} = \sqrt{169} =13$ .

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

$\frac{X}{12} = \frac{12}{13}$

$\frac{X}{12}\cdot 12 = \frac{12}{13} \cdot 12$

$X = \frac{144}{13} = 11\frac{1}{13}$

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Example Question #1 : Triangles

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

Possible Answers:

$32\text{cm}$

$48\text{cm}$

$\text{There is not enough information to solve the problem.}$

$64\text{cm}$

$56\text{cm}$

Correct answer:

$48\text{cm}$

Explanation:

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

P = a+b+c

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

$P = 16\text{cm} +16\text{cm} +16\text{cm}$

$P = 48\text{cm}$

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Example Question #2 : Triangles

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

Possible Answers:

$14\text{in}$

$12\text{in}$

$9\text{in}$

$11\text{in}$

$13\text{in}$

Correct answer:

$12\text{in}$

Explanation:

The formula to find the perimeter of an equilateral triangle is

P = 3a

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

$36\text{in} = 3a$

$\frac{36\text{in}}{3} = \frac{3a}{3}$

$12\text{in} = a$

$a = 12\text{in}$

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

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Example Question #3 : Triangles

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

Possible Answers:

$34\text{in}$

$51\text{in}$

$28\text{in}$

$42\text{in}$

$48\text{in}$

Correct answer:

$51\text{in}$

Explanation:

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

P = a+b+c

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

$P = 17\text{in} +17\text{in} +17\text{in}$

$P = 51\text{in}$

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Example Question #4 : Triangles

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

Possible Answers:

$36\text{in}$

$18\text{in}$

$33\text{in}$

$23\text{in}$

$32\text{in}$

Correct answer:

$23\text{in}$

Explanation:

The formula to find the perimeter of an equilateral triangle is

P = 3a

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

$69\text{in} = 3a$

$\frac{69\text{in}}{3} = \frac{3a}{3}$

$23\text{in} = a$

$a = 23\text{in}$

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

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Example Question #181 : 2 Dimensional Geometry

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

Possible Answers:

$13\text{cm}$

$15\text{cm}$

$14\text{cm}$

$16\text{cm}$

$12\text{cm}$

Correct answer:

$14\text{cm}$

Explanation:

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

P = 3a

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

$42\text{cm} = 3a$

$\frac{42\text{cm}}{3} = \frac{3a}{3}$

$14\text{cm} = a$

$a = 14\text{cm}$

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

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Example Question #5 : Perimeter And Sides Of Triangles

A triangle has the sides of (x+1) , (1-2x) , and (3x-1) . What is the perimeter of the triangle?

Possible Answers:

-5x+3

2x-1

-2x+1

5x-3

2x+1

Correct answer:

2x+1

Explanation:

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

(x+1)+ (1-2x)+(3x-1) = 2x+1

The answer is: 2x+1

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Example Question #182 : Geometry And Graphs

Suppose the perimeter of a triangle is $\frac{1}{3}x-9$ . What must be the side length?

Possible Answers:

3x -27

$\frac{1}{9}x -9$

$\frac{1}{9}x -3$

3x-9

$\frac{1}{9}x +9$

Correct answer:

$\frac{1}{9}x -3$

Explanation:

There are three sides in a triangle.

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

$\frac{1}{3}(\frac{1}{3}x-9) = \frac{1}{9}x -3$

The answer is: $\frac{1}{9}x -3$

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Example Question #182 : Geometry And Graphs

The perimeter of an equilateral triangle is 45in. Find the length of one side.

Possible Answers:

$13\text{in}$

$\text{There is not enough information to solve the problem.}$

$12\text{in}$

$10\text{in}$

$15\text{in}$

Correct answer:

$15\text{in}$

Explanation:

The formula to find the perimeter of an equilateral triangle is

P = 3a

Now, we know the perimeter of the triangle is 45in. So, we can substitute and solve for a. So, we get

$45\text{in} = 3a$

$\frac{45\text{in}}{3} = \frac{3a}{3}$

$15\text{in} = a$

$a = 15\text{in}$

Therefore, the length of one side of the equilateral triangle is 15in.

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Example Question #11 : Triangles

An equilateral triangle has a perimeter of 123in. Find the length of one side.

Possible Answers:

$14\text{in}$

$41\text{in}$

$29\text{in}$

$33\text{in}$

$36\text{in}$

Correct answer:

$41\text{in}$

Explanation:

The formula to find the perimeter of an equilateral triangle is

P = 3a

where a is the length of one side of the triangle. 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 123in. So, we will substitute and solve for a. We get

$123\text{in} = 3a$

$\frac{123\text{in}}{3} = \frac{3a}{3}$

$41\text{in} = a$

$a = 41\text{in}$

Therefore, the length of one side of the equilateral triangle is 41in.

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Perimeter And Sides Of Triangles

Example Question #1 : Triangles

Example Question #2 : Triangles

Example Question #3 : Triangles

Example Question #4 : Triangles

Example Question #181 : 2 Dimensional Geometry

Example Question #5 : Perimeter And Sides Of Triangles

Example Question #182 : Geometry And Graphs

Example Question #182 : Geometry And Graphs

Example Question #11 : Triangles

All GED Math Resources

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