Question

ps is the midsegment of the trapezoid qrtu. if tu = 11 and ps = 16, what is qr? qr =

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment of a trapezoid is $PS=\frac{QR + TU}{2}$, where $PS$ is the mid - segment, $QR$ and $TU$ are the bases of the trapezoid.

Step2: Rearrange the formula to solve for $QR$

Multiply both sides of the equation $PS=\frac{QR + TU}{2}$ by 2: $2PS=QR + TU$. Then, subtract $TU$ from both sides: $QR = 2PS−TU$.

Step3: Substitute the given values

Given $TU = 11$ and $PS = 16$, substitute these values into the formula $QR = 2PS−TU$. So, $QR=2\times16 - 11$.

Step4: Calculate the value of $QR$

First, calculate $2\times16=32$. Then, $32−11 = 21$.

Answer:

$21$