What is the value of x in parallelogram upper Q upper R upper S upper T?
Parallelogram upper Q upper R upper S upper T is shown with diagonals upper Q upper S and upper R upper T drawn. Part of diagonal upper Q upper S is labeled 8, and the other part is labeled 2 x. Part of diagonal upper R upper T is labeled 3 x, and the other part is labeled 12.
(1 point)
Responses
16
16
12
12
8
8
4
The value of x in parallelogram QRST is 4.
To find the value of x in parallelogram QRST, we need to use the fact that in a parallelogram, opposite sides are equal in length.
We are given that part of diagonal QS is labeled 8, and the other part is labeled 2x. We also know that part of diagonal RT is labeled 3x, and the other part is labeled 12.
Since QS is a diagonal of the parallelogram, it is equal in length to RT.
We can set up the equation: 8 + 2x = 3x + 12
Now, we can solve for x:
8 + 2x - 2x = 3x - 2x + 12
8 = x + 12
Subtracting 12 from both sides:
8 - 12 = x + 12 - 12
-4 = x
Therefore, the value of x in parallelogram QRST is -4.
To find the value of x in parallelogram QRST, we can use the fact that opposite sides of a parallelogram are equal in length.
From the given information, we know that part of diagonal QS is labeled 8 and the other part is labeled 2x. Similarly, part of diagonal RT is labeled 3x and the other part is labeled 12.
Since QS and RT are diagonals of the parallelogram, they bisect each other. This means that the sum of the parts of the diagonals is equal. So, we can set up the following equation:
8 + 2x = 3x + 12
By simplifying and rearranging the equation, we get:
8 + 12 = 3x - 2x
20 = x
Therefore, the value of x in parallelogram QRST is 20.