triangle STR is an equilateral triangle. What is the value of x if the measures of the sides ate 7x+5,4x+14, and 10x-4 ?

x=3, sides are 26

x=root[3]{26}=2.9625

To find the value of x in an equilateral triangle, we need to set the measures of all three sides equal to each other and solve for x.

Given that the measures of the sides are 7x+5, 4x+14, and 10x-4, we can set up the equation:

7x+5 = 4x+14 = 10x-4

Now, let's solve the equation step by step:

1. Equate the first two sides:
7x+5 = 4x+14

2. Subtract 4x from both sides to isolate the x term:
7x - 4x + 5 = 14

3. Simplify:
3x + 5 = 14

4. Subtract 5 from both sides:
3x = 14 - 5

5. Simplify:
3x = 9

6. Divide both sides by 3 to solve for x:
x = 9/3

7. Simplify:
x = 3

Therefore, the value of x is 3.