Two sides of an equilateral triangle have lengths x+2 and -2x+20 which could be the length of the third side:14-x or 2x+4?
A. 14-xonly
B. Both 14x and 2x+4
C. 2x+4 only.
D. Neither 14-x nor 2x+4
x+2 = -2x + 20
3 x = 18
x = 6
so side = 8
14 - 8 = 8 so 14-x works
and 2x + 4 is not 8
Well, well, well. It seems we have ourselves a little triangle conundrum here. Let me put on my mathematician clown hat and solve this riddle for you.
Let's start by considering the sum of the lengths of any two sides of an equilateral triangle. In our case, if the first two sides have lengths x+2 and -2x+20, we get:
(x+2) + (-2x+20) = -x + 22
Now, for it to be an equilateral triangle, the third side should have the same length as well. So we need to find out whether -x+22 is equal to 14-x or 2x+4.
Let's do some simple math:
If -x+22 equals 14-x, we can simplify it to:
22 = 14
Hmm, something seems fishy here. Clearly, 22 is not equal to 14, unless we're operating in the Twilight Zone.
Now, let's try the other option:
If -x+22 equals 2x+4, we can simplify it to:
3x = 18
Dividing both sides by 3 gives us:
x = 6
Ah-ha! We've found the solution! So, the length of the third side is 2x+4, which becomes 2(6)+4, or 16.
Therefore, the correct answer is C) 2x+4 only.
And that, my friend, is how you solve a clown-approved triangle puzzle!
To determine which length could be the length of the third side of the equilateral triangle, we need to use the property of an equilateral triangle where all sides are equal.
Let's start by setting up an equation to represent this property:
x+2 = -2x+20
Next, we can add 2x to both sides to get rid of the -2x term:
x+2x+2 = -2x+2x+20
Simplifying further:
3x+2 = 20
Now, subtract 2 from both sides:
3x = 18
Finally, divide both sides by 3:
x = 6
Now that we have the value of x, we can substitute it back into the expressions for the possible third side lengths:
For 14-x, we have:
14 - 6 = 8
For 2x+4, we have:
2(6) + 4 = 12 + 4 = 16
Comparing these values to the given side lengths, we find that:
- The length 8 (14-x) matches the length x+2 of one side (x+2).
- The length 16 (2x+4) does not match the length -2x+20.
Therefore, the correct answer is:
A. 14-x only
To determine which length could be the length of the third side of the equilateral triangle, we need to use the property of an equilateral triangle.
In an equilateral triangle, all three sides have the same length.
Given the lengths of two sides, x+2 and -2x+20, we can set up an equation to find the value of x.
According to the property of an equilateral triangle, the length of the third side should be the same as the other two sides.
Therefore, we can set up the following equation:
x + 2 = -2x + 20
To solve for x, we can start by isolating the variable terms on one side:
x + 2x = 20 - 2
Combining like terms gives us:
3x = 18
Now, we can solve for x by dividing both sides of the equation by 3:
x = 6
Now that we have found the value of x, we can substitute it into the expressions for the lengths of the third side:
For the expression 14 - x:
14 - 6 = 8
For the expression 2x + 4:
2(6) + 4 = 12 + 4 = 16
Comparing these values to the lengths of the given side lengths:
8 is not equal to x + 2 (which is 6 + 2)
16 is not equal to -2x + 20 (which is -12 + 20)
Therefore, neither 14 - x nor 2x + 4 could be the length of the third side.
So, the correct answer is D. Neither 14 - x nor 2x + 4.