Question

given that the quadrilateral qrst is a parallelogram, $overline{qr}=6x - 14$ and $overline{st}=7x - 21$, what is $overline{qr}$?

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, $\overline{QR}=\overline{ST}$. Set up the equation $6x - 14=7x - 21$.

Step2: Solve for x

Subtract $6x$ from both sides of the equation: $-14=x - 21$. Then add 21 to both sides: $x = 7$.

Step3: Find $\overline{QR}$

Substitute $x = 7$ into the expression for $\overline{QR}$. $\overline{QR}=6x - 14=6\times7-14=42 - 14 = 28$.

Answer:

28