Question

The diagonals of parallelogram QRST intersect at point U. If TU = 9x - 1 and RU = 5x + 3, what is TU? o 1 o 5 o 8 o 13

Answer 1

The length of TU can be found by setting up an equation using the fact that the diagonals of a parallelogram bisect each other. Solving this equation yields the value of x, which can then be substituted back into the equation to find the length of TU. The length of TU is 41/13.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, meaning they intersect at a point that divides each diagonal into two equal segments. We can set up an equation using the given information to find the length of TU. Since the diagonals bisect each other, TU is equal to half of the diagonal RU.

TU = 1/2 * RU

Substituting the values given: 9x - 1 = 1/2 * (5x + 3)

Solving the equation:

1. 9x - 1 = 1/2 * 5x + 1/2 * 3
2. 9x - 1 = 5/2 * x + 3/2
3. 9x - 1 - 5/2 * x = 3/2
4. 9x - 5/2 * x = 3/2 + 1
5. 18x - 5x = 4 + 2
6. 13x = 6
7. x = 6/13

Now, we can substitute the value of x back into the equation for TU:

TU = 9 * (6/13) - 1

TU = 54/13 - 13/13

TU = 41/13

So, the length of TU is 41/13.

Learn more about Parallelogram diagonals

Answer 2

Answer: 1

Step-by-step explanation:

9x-1=5x+3

9x-1+1=5x+3+1

9x=5x+4

9x-5x=5x+4-5

4x=4

4x/4=4/4

x=1