Question

If RU= 8y and TU = y + 28, find the value of y that makes quadrilateral QRST a

parallelogram.
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Answer 1

To make QRST a parallelogram, we equate the lengths of opposite sides RU and TU, leading to the equation 8y = y + 28. Solving for y gives us y = 4, which is the required value to make QRST a parallelogram.

Step-by-step explanation:

To determine the value of y that makes quadrilateral QRST a parallelogram, we must use the properties of a parallelogram. One property is that opposite sides are equal in length. Thus, if RU and TU are opposite sides of a parallelogram, then their lengths must be equal when QRST is a parallelogram.

We are given that RU = 8y and TU = y + 28. We can set these two expressions equal to each other to find the value of y:

RU = TU
8y = y + 28

Now we solve for y:

8y - y = 28
7y = 28
y = 28/7
y = 4

Therefore, y must be 4 to make QRST a parallelogram.