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

Relevance
• 4 weeks ago

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.

• 4 weeks ago

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

• 1 month ago

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.

• Elaine
Lv 7
1 month ago

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.

• Ian H
Lv 7
1 month ago

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.

• 1 month ago

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.

• 1 month ago

3x - 4 = 5x - 8

x = 2

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

Hence the triangle is not equilateral.

• 1 month ago

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

x=2, x=5, x=11

Not an equilateral triangle.

• 1 month ago

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.

• rotchm
Lv 7
1 month ago

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?

Dont forget to vote me best answer for being the first to correctly walk you through and especially for not spoiling out the answer!