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A square rug border consists of a consistent pattern of it is provided triangles, v isosceles triangles as corners, among which is displayed above. If the size of every equilateral triangle next is 5 inches, and there room 40 triangles in total, what is the full perimeter that the rug?

The inner angles of the edge triangles is 30°.

You are watching: What is the perimeter of a equilateral triangle


Explanation:

There room 2 components to this problem. The first, and also easier one, is recognizing how much of the perimeter the it is intended triangles take it up—since there are 40 triangle in total, there need to be 40 – 4 = 36 of these triangles. Through observation, every contributes just 1 side to the in its entirety perimeter, therefore we can simply multiply 36(5) = 180" contribution.

The second component is the edge triangles—recognizing that the congruent sides are surrounding to the 5-inch it is intended triangles, and the congruent angles have the right to be discovered by

180 = 30+2x → x = 75°

We deserve to use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2"".

Since there space 4 corners to the square rug, 2(4) = 8"" donation to the full perimeter. Adding the 2 components, we acquire 180+8 = 188 inch perimeter.


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Example inquiry #2 : exactly how To discover The Perimeter the An it is intended Triangle


The height of an it is intended triangle is

*

What is the triangle"s perimeter?


Possible Answers:

8


*


6


24


12


Correct answer:

12


Explanation:
*
 

*

Using this ratio, we discover that the size of this triangle"s hypotenuse is 4. Hence the perimeter of the it is provided triangle will certainly be 4 multiply by 3, i beg your pardon is 12.


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Example inquiry #3 : how To uncover The Perimeter of An it is provided Triangle


An it is intended triangle has actually a side size of 

*
. What is that perimeter?


Possible Answers:

Not enough information to solve.


*


*


*


Correct answer:

*


Explanation:

An it is provided triangle possesses three sides of same lengths. Therefore, us can easily calculate that is perimeter through tripling the provided side length.

*

*

*


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Example concern #4 : just how To discover The Perimeter the An it is provided Triangle


An equilateral triangle has an altitude length of 

*
. What is the perimeter?


Possible Answers:

Not enough information come solve


Correct answer:

*


Explanation:

An altitude slices an it is provided triangle into two 

*
 triangles. These triangles follow a side size pattern. The smallest of the two legs equals 
*
and the hypotenuse equals 
*
. By method of the Pythagorean Theorem, the longest leg or 
*
.

We have actually the length of the altitude that the triangle 

*
. We have the right to solve because that the the smallest side 
*
 via substitution and straightforward algebra.

*

*

*

*

Note, this is only the smallest side of one of the 

*
triangles. It needs to be double to equal a finish side that the equilateral triangle.

*

*

Now, the side length have the right to be tripled to calculation the perimeter.

*

*

*


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Example question #5 : exactly how To discover The Perimeter the An it is intended Triangle


Find the perimeter that the following equilateral triangle:

*


Possible Answers:
Correct answer:

*


Explanation:

The formula for the perimeter that an equilateral triangle is:

*

Where 

*
 is the size of the side

Plugging in ours values, we get:

*


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Example question #6 : exactly how To find The Perimeter the An it is provided Triangle


Determine the perimeter the the adhering to equilateral triangle:


Possible Answers:
Correct answer:

*


Explanation:

The formula because that the perimeter the an it is provided triangle is:

*
,

where 

*
 is the size of the side.

Plugging in our value, we get:

*


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Example inquiry #7 : just how To find The Perimeter that An it is provided Triangle


An equilateral triangle has a next of size

*
 feet. What is the perimeter the the triangle? 


Possible Answers:

 feet 


It can not be determined from the information given. 


*
 feet 


*
 foot


*
 feet 


Correct answer:

 feet 


Explanation:

An it is intended triangle through definition. Has three congruent sides. Thus, if one side is

*
 feet long, climate all three sides room each
*
 feet long. We additionally know the the perimeter is the sum of every sides. Therefore, our perimeter is
*
 

Since we were given units that feet, our last answer is

*
 feet. 


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