if triangle ABC is equilateral with AB = 2x, BC = 4x - 7, and x + 3.5, then what is x?
If it is equilateral,AB=BC
2x=4x-7
subtract 2x from each side, and add 7 to each side.
7=2x
divide each side by 2
x=3.5
To find the value of x, we can set up an equation using the given information.
Since triangle ABC is equilateral, it means that all three sides are equal.
We are given that AB = 2x, BC = 4x - 7, and AC = x + 3.5.
Using the fact that all three sides are equal, we can set up an equation:
AB = BC = AC
2x = 4x - 7 = x + 3.5
Now, we'll solve this equation step-by-step:
2x = 4x - 7
Subtract 2x from both sides:
2x - 2x = 4x - 7 - 2x
0 = 2x - 7
Add 7 to both sides:
0 + 7 = 2x - 7 + 7
7 = 2x
Divide both sides by 2:
7/2 = 2x/2
7/2 = x
Therefore, x is equal to 7/2 or 3.5.
To find the value of x, we can use the given information about the lengths of the sides of the equilateral triangle ABC.
An equilateral triangle has all three sides of equal length. Therefore, AB = BC = AC.
According to the given information:
AB = 2x
BC = 4x - 7
AC = x + 3.5
Since AB = BC, we can equate their expressions:
2x = 4x - 7
To solve for x, let's isolate the x term by moving the constant term to the other side of the equation:
7 = 4x - 2x
Simplifying the equation:
7 = 2x
To obtain the value of x, divide both sides of the equation by 2:
7/2 = x
Therefore, x = 3.5.