Question

if $qr = c + 15$ and $qt = 2c + 5$, find $qt$ in parallelogram $rstu$.
$qt = \square$

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, the diagonals bisect each other. So \( QR = QT \).

Step2: Set up equation

Since \( QR = c + 15 \) and \( QT = 2c + 5 \), and \( QR = QT \), we have \( c + 15 = 2c + 5 \).

Step3: Solve for \( c \)

Subtract \( c \) from both sides: \( 15 = c + 5 \). Then subtract 5 from both sides: \( c = 15 - 5 = 10 \).

Step4: Find \( QT \)

Substitute \( c = 10 \) into \( QT = 2c + 5 \): \( QT = 2(10) + 5 = 20 + 5 = 25 \).

Answer:

25