ACT Math Help » Geometry » Plane Geometry » Triangles » Equilateral Triangles

What is the perimeter of an equilateral triangle with an area of

?

Explanation:

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both

triangles. Therefore, you can create a ratio to help you find

.

You are watching: Can an equilateral triangle be a right triangle

The ratio of the small base to the height is the same as

. Therefore, you can write the following equation:

This means that

.

Now, the area of a triangle can be written:

, and based on our data, we can replace

with

. This gives you:

Now, let”s write that a bit more simply:

Solve for

. Begin by multiplying each side by

:

Divide each side by

:

Finally, take the square root of both sides. This gives you

. Therefore, the perimeter is

.

Report an Error

### Example Question #145 : Act Math

An equilateral triangle with a perimeter of

has sides with what length?

**Possible Answers:**

**Correct answer:**

Explanation:

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

Report an Error

### Example Question #146 : Act Math

Jill has an equilateral triangular garden with a base of

and one leg with a length of

, what is the perimeter?

**Possible Answers:**

**Correct answer:**

Explanation:

Since the triangle is equilateral, the base and the legs are equal, so the first step is to set the two equations equal to each other. Start with

, add

to both sides giving you

. Subtract

from both sides, leaving

. Finally divide both sides by

, so you”re left with

. Plug

back in for

into either of the equations so that you get a side length of

. To find the perimeter, multiply the side length

, by

, giving you

.

Report an Error

### Example Question #151 : Plane Geometry

Find the perimeter of an equilateral triangle whose side length is

**Possible Answers:**

**Correct answer:**

Explanation:

To find perimeter of an quilateral triangle, simply multiply the side length by

. Thus,

Report an Error

### Example Question #152 : Plane Geometry

Find the perimeter of an equilateral triangle whose side length is

.

**Possible Answers:**

**Correct answer:**

Explanation:

To solve, simply multiply the side length by

. Thus,

Report an Error

### Example Question #153 : Plane Geometry

Find the perimeter of an equilateral triangle given side length of 2.

See more: How Much Is 2 Pounds Of Potatoes In A Pound? How Many Cups Of Potato In 2 Pounds

**Possible Answers:**

**Correct answer:**

Explanation:

To solve, simply multiply the side length by 3 since they are all equal. Thus,

Report an Error

### Example Question #3 : How To Find The Height Of An Equilateral Triangle

What is the height of an equilateral triangle with a side length of 8 in?

**Possible Answers:**

**Correct answer:**

Explanation:

An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees.

To find the height we divide the triangle into two special 30 – 60 – 90 right triangles by drawing a line from one corner to the center of the opposite side. This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. The special right triangle gives side ratios of

,

, and

. The hypoteneuse, the side opposite the 90 degree angle, is the full length of one side of the triangle and is equal to

. Using this information, we can find the lengths of each side fo the special triangle.

The side with length

will be the height (opposite the 60 degree angle). The height is

inches.

Report an Error

### Example Question #1 : How To Find The Height Of An Equilateral Triangle

Find the height of a triangle if all sides have a length of

.

**Possible Answers:**

**Correct answer:**

Explanation:

Draw a vertical line from the vertex. This will divide the equilateral triangle into two congruent right triangles. For the hypothenuse of one right triangle, the length will be

. The base will have a dimension of

. Use the Pythagorean Theorem to solve for the height, substituting in

for

, the length of the hypotenuse, and

for either

or

, the length of the legs of the triangle:

Report an Error

### Example Question #1 : How To Find The Height Of An Equilateral Triangle

What is the height of an equilateral triangle with sides of length

?

**Possible Answers:**

**Correct answer:**

Explanation:

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both

triangles. Therefore, you can create a ratio to help you find

.

The ratio of

to

is the same as the ratio of

to

.

As an equation, this is written:

Solving for

, we get:

Report an Error

### Example Question #3 : How To Find The Height Of An Equilateral Triangle

The Triangle Perpendicular Bisector Theorem states that the perpendicular bisector of an equilateral triangle is also the triangle”s height.

See more: How Much Is Richie Sambora Worth, What Is Richie Samboras Net Worth

is an equilateral triangle with side length

inches. What is the height of

?

**Possible Answers:**

**Correct answer:**

Explanation:

To calculate the height of an equilateral triangle, first draw a perpendicular bisector for the triangle. By definition, this splits the opposite side from the vertex of the bisector in two, resulting in two line segments of length

inches. Since it is perpendicular, we also know the angle of intersection is

.

So, we have a new right triangle with two side lenghts

and

for the hypotenuse and short leg, respectively. The Pythagorean theorem takes over from here:

—>

So, the height of our triangle is

.

Report an Error

← Previous *1* 2 Next →

View ACT Math Tutors

Amber Certified Tutor

University of Massachusetts-Lowell, Bachelor of Science, Physics.

View ACT Math Tutors

Adesola Certified Tutor

University of West Georgia, Master of Science, Mathematics Teacher Education.

View ACT Math Tutors

Joseph Certified Tutor

Truman State University, Bachelors, Mathematics, Theatre.

### All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutoring in Top Cities:

Atlanta ACT Math Tutoring, Austin ACT Math Tutoring, Boston ACT Math Tutoring, Chicago ACT Math Tutoring, Dallas Fort Worth ACT Math Tutoring, Denver ACT Math Tutoring, Houston ACT Math Tutoring, Kansas City ACT Math Tutoring, Los Angeles ACT Math Tutoring, Miami ACT Math Tutoring, New York City ACT Math Tutoring, Philadelphia ACT Math Tutoring, Phoenix ACT Math Tutoring, San Diego ACT Math Tutoring, San Francisco-Bay Area ACT Math Tutoring, Seattle ACT Math Tutoring, St. Louis ACT Math Tutoring, Tucson ACT Math Tutoring, Washington DC ACT Math Tutoring

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in Miami, Spanish Courses & Classes in Miami, SSAT Courses & Classes in Miami, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle, MCAT Courses & Classes in Philadelphia, ACT Courses & Classes in Los Angeles, LSAT Courses & Classes in Atlanta, LSAT Courses & Classes in Miami, ISEE Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in Seattle, MCAT Test Prep in Philadelphia, LSAT Test Prep in Atlanta, SAT Test Prep in Phoenix, SAT Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in New York City, SSAT Test Prep in Houston, LSAT Test Prep in Washington DC, GMAT Test Prep in Philadelphia

Report an issue with this question

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.

Do not fill in this field

* Your Name:

* Issue Description:

DMCA Complaint

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

Please follow these steps to file a notice:

You must include the following:

Send your complaint to our designated agent at:

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

## Discussion about this post