in triangle PQR below, S and T are midpoints of side PQ and QR, repectively.If ST=12 and PR=2X+4, what is te value of X
To find the value of X, we can use the fact that S and T are midpoints of PQ and QR, respectively.
Since S and T are midpoints, we can imply that ST is equal to half of the length of PR. Therefore:
ST = 1/2 * (PR)
Given that ST is 12 and PR is 2X + 4, we can set up the equation:
12 = 1/2 * (2X + 4)
To solve for X, let's first multiply both sides of the equation by 2 to remove the fraction:
2 * 12 = 2 * (1/2) * (2X + 4)
24 = 2X + 4
Next, let's isolate the variable X by subtracting 4 from both sides:
24 - 4 = 2X + 4 - 4
20 = 2X
Finally, let's solve for X by dividing both sides by 2:
20/2 = 2X/2
10 = X
Therefore, the value of X is 10.
To find the value of X, we need to use the information given about the midpoints in the triangle PQR.
We know that S and T are the midpoints of sides PQ and QR, respectively. This means that ST is half the length of PR.
Given that ST = 12, we can say that PR = 2 * ST.
Substituting the value of ST into the equation, we get:
PR = 2 * 12
PR = 24
Since PR = 2X + 4, we can set up the equation:
2X + 4 = 24
Now, we can solve for X:
2X = 24 - 4
2X = 20
Dividing both sides of the equation by 2:
X = 20 / 2
X = 10
Therefore, the value of X is 10.