# Is there a value for x when the given triangle is equilateral? Relevance

You can equate two sides to immediately find the value of x since each side is equal to the other.

2x + 7 = 5x - 8

3x = 15

x = 5

But to further check if the triangle is really an equilateral triangle, substitute the value of x to each side.

2x + 7 = 17

5x - 8 = 17

3x - 4 = 11

Thus, the triangle is not an equilateral triangle since one side is not equal to the other two. This is actually an isosceles triangle.

• equilateral implies all three sides are equal

so 3x -4 = 5x - 8

==> 2x= 4

==> x = 2

so 3x- 4 = 2

5x-8 = 2

but 2x + 7 = 11

so, no, the triangle can't be equilateral for any real value of x

• If the 3 sides equal, then

3x-4=5x-8=2x+7

=>

x-4=3x-8=7

=>

x=11 & x=5

=>

11=5 which is false.

So the triangle can't be equilateral.

• Since this is supposed to be an equilateral triangle all sides are equal.  Take any 2 equations and rewrite as a single equation and solve for x

3x - 4 = 5x - 8

-4 + 8 = 5x - 3x

4 = 2x

2 = x

Substitute the value of x into the three equations and solve

2x + 7

2(2) + 7 = 11

5x - 8

5(2) - 8 = 2

3x - 4

3(2) - 4 = 2

Since all three sides are not equal the triangle is not equilateral.

• Solutions for selected pairs of sides differ, so an isosceles is possible,

but not an equilateral which would require all three pairs to have same solution.

• construct an equation to solve for x..Since all sides of the sides of equilateral are the same, we make 2 unknown side equal to each other.

3x - 4 = 5x - 8

3x - 5x = - 8 + 4

- 2x = - 4

x = 2

3x + 4 = 3(2) + 4 = 10

2x + 7 = 2(2) + 7 = 11

5x - 8 = 5(2) - 8 =

Since all the sides are not the same, therefore it is not a equilateral triangle.

• 3x - 4 = 5x - 8

x = 2

2x + 7 is the base, which equals 11.

Hence the triangle is not equilateral.

• Taken two at a time :  3x-4=5x-8  x=2...

x=2, x=5, x=11

Not an equilateral triangle.

• It's impossible for that to be an equilateral triangle.

Let's assume that the top two sides are equal:

5x - 8 = 3x - 4

2x = 8 - 4

2x = 4

x = 4/2

x = 2

3x - 4 --> 3(2) - 4 = 2 units

5x - 8 --> 5(2) - 8 = 2 units

But the bottom sides is:

2x + 7 --> 2(2) + 7 = 11 units

There is no value of x that will make that an equilateral triangle.

UPDATE:

Perhaps the sides were supposed to be:

4x - 3 <-- notice the switch

5x - 8

2x + 7

In that case x = 5 and each side is 17 units.

• Equilateral means all sides have the same lengths.

So lets see/force the two sides to be the same: 3x-4 = 5x-8.

What must x be? And what is teh length of those two sides then?

Now, verify with this x if the bottom side has the same length as the other two.

Conclusion?

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