If the area of an equilateral triangle is 9√3 cm 2 what is the length of the side of the triangle

The area of an equilateral triangle is

Possible Answers:

Correct answer:

Explanation:

An equilateral triangle can be broken down into 2 30-60-90 right triangles (see image). The length of a side (the base) is 2x while the length of the height is

Therefore, if 

A length of the side equals 2x:

What is the area of this triangle if 

Possible Answers:

Correct answer:

Explanation:

We know the formula for the area of an equilateral triangle is:

if 

So, since we are told that 

Find 

Possible Answers:

Correct answer:

Explanation:

This triangle is equilateral; we can tell because each of its sides are the same length, 

What is side 

Possible Answers:

Correct answer:

Explanation:

Since each of this triangle's sides is equal in length, it is equilateral. To find the length of one side of an equilateral triangle, we need to divide the perimeter by 

The height of the triangle is

What is the length of the base of the triangle to the nearest tenth?

Possible Answers:

Correct answer:

Explanation:

Since it is an equilateral triangle, the line that represents the height bisects it into a 30-60-90 triangle.

Here you may use

Use the definition of an equilateral triangle to know that the answer of the hypotenuse also applies to the base of the triangle.

Therefore,

The height of an equilateral triangle is 5. How long are its sides?

Possible Answers:

Correct answer:

Explanation:

The height of an equilateral triangle, shown by the dotted line, is also one of the legs of a right triangle:

The hypotenuse is x, the length of each side in this equilateral triangle, and then the other leg is half of that, 0.5x. 

To solve for x, use Pythagorean Theorem:

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square, as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

Andrew
Certified Tutor

University of South Florida-Main Campus, Bachelors, Biomedical Sciences. New York Medical College, PHD, Doctor of Medicine.

Megan
Certified Tutor

University of Portland, Bachelor in Arts, Communication, General. Liberty University, Master of Science, Business Administrat...

Jason
Certified Tutor

NJCU, Bachelor in Arts, Communication, General. Saint Peters College, Masters in Business Administration, Elementary and Midd...

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below: