ACT Math aid » Geometry » aircraft Geometry » triangle » Equilateral triangles

What is the perimeter that an it is provided triangle with an area of 

*
?


*


*


*


*


Explanation:

Recall the from any kind of vertex of an it is provided triangle, you can drop a elevation that is a bisector of that vertex as well together a bisector the the correlative side. This offers you the complying with figure:

*

Notice the the small triangles in ~ the bigger triangle are both 

*
 triangles. Therefore, friend can develop a proportion to help you find 
*
.

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The ratio of the little base come the elevation is the exact same as 

*
. Therefore, you can write the complying with equation:

*

This way that 

*
.

Now, the area that a triangle can be written:

*
, and based on ours data, we can replace 
*
 with 
*
. This gives you:

*

Now, let"s create that a bit much more simply:

*

Solve for 

*
. Start by multiplying each side by 
*
:

*

Divide each side by 

*
:

*

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

*
. Therefore, the perimeter is 
*
.


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Example inquiry #1 : Equilateral triangles


An equilateral triangle v a perimeter of

*
 has sides with what length?


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle has 3 equal size sides.

Therefore the perimeter equation is as follows,

*
.

So division the perimeter by 3 to discover the size of every side.

Thus the price is:

*

*

*


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Example question #1 : Equilateral triangle


Jill has actually an equilateral triangular garden through a base of

*
 and one leg v a length of
*
, what is the perimeter? 


Possible Answers:
Correct answer:

*


Explanation:

Since the triangle is equilateral, the base and the legs are equal, for this reason the very first step is to set the 2 equations equal to every other. Start with

*
, add
*
 to both sides offering you
*
. Subtract
*
 from both sides, leaving
*
. Finally divide both political parties by
*
, so you"re left v
*
. Plug
*
 back in because that
*
into either of the equations so that you get a side size of
*
. To find the perimeter, main point the side size
*
, by
*
, giving you
*
.


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Example inquiry #1 : Equilateral triangles


Find the perimeter that an it is provided triangle whose side length is 

*


Possible Answers:
Correct answer:

*


Explanation:

To uncover perimeter of one quilateral triangle, simply multiply the side size by

*
. Thus,

*


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Example concern #2 : Equilateral triangles


Find the perimeter that an it is intended triangle who side size is

*
.


Possible Answers:
Correct answer:

*


Explanation:

To solve, just multiply the side size by

*
. Thus,

*


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Example concern #2 : how To uncover The Perimeter that An it is intended Triangle


Find the perimeter that an it is provided triangle offered side length of 2.


Possible Answers:
Correct answer:

*


Explanation:

To solve, just multiply the side length by 3 due to the fact that they room all equal. Thus,

*


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Example question #1 : Equilateral triangle


What is the elevation of an it is intended triangle with a side size of 8 in?


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle has three congruent sides, and is additionally an equiangular triangle with three congruent angle that each meansure 60 degrees.

To find the elevation we divide the triangle into two unique 30 - 60 - 90 appropriate triangles by illustration a heat from one corner to the center of the contrary side. This segment will be the height, and will be opposite from among the 60 level angles and adjacent to a 30 level angle. The special appropriate triangle provides side ratios the

*
,
*
, and also
*
. The hypoteneuse, the side opposite the 90 degree angle, is the complete length the one side of the triangle and is same to
*
. Making use of this information, us can uncover the lengths of each side fo the special triangle.

*

The next with size

*
will be the elevation (opposite the 60 degree angle). The elevation is
*
inches.


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Example inquiry #1 : just how To discover The height Of An equilateral Triangle


Find the elevation of a triangle if every sides have actually a length of

*
.


Possible Answers:
Correct answer:

*


Explanation:

Draw a vertical heat from the vertex. This will certainly divide the equilateral triangle right into two congruent appropriate triangles. Because that the hypothenuse that one right triangle, the length will it is in

*
. The base will have actually a dimension of
*
. Use the Pythagorean organize to settle for the height, substituting in 
*
 for 
*
, the size of the hypotenuse, and 
*
 for either 
*
 or 
*
, the length of the legs of the triangle:

*

*

*

*

*


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Example concern #2 : exactly how To discover The elevation Of An equilateral Triangle


What is the elevation of an equilateral triangle v sides the length 

*
?


Possible Answers:
Correct answer:

*


Explanation:

Recall the from any kind of vertex that an equilateral triangle, you can drop a height that is a bisector of the vertex as well together a bisector of the correlative side. This offers you the adhering to figure:

*

Notice the the tiny triangles in ~ the larger triangle space both 

*
 triangles. Therefore, you can create a proportion to help you find 
*
.

The proportion of 

*
 to 
*
 is the same as the proportion of 
*
 to 
*
.

As one equation, this is written:

*

Solving for 

*
, we get: 
*


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Example question #3 : just how To find The elevation Of An equilateral Triangle


The Triangle Perpendicular Bisector Theorem says that the perpendicular bisector of an it is intended triangle is also the triangle"s height.


*
 is an it is provided triangle with side length 
*
 inches. What is the elevation of
*
?


Possible Answers:
Correct answer:

*


Explanation:

To calculation the elevation of an equilateral triangle, an initial draw a perpendicular bisector because that the triangle. By definition, this splits the opposite side from the crest of the bisector in two, causing two line segments that length 

*
 inches. Because it is perpendicular, we likewise know the angle of intersection is 
*

So, we have actually a brand-new right triangle v two side lenghts 

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

*
 ---> 
*

So, the height of our triangle is 

*
.


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