Question

given pqrs is a rectangle, sq = 11x - 26, and pr = 5x + 28. find pr.
pr =

Explanation:

Step1: Recall rectangle diagonals property

In a rectangle, diagonals are equal. So \( SQ = PR \).

Step2: Set up equation

Substitute \( SQ = 11x - 26 \) and \( PR = 5x + 28 \) into \( SQ = PR \):
\( 11x - 26 = 5x + 28 \)

Step3: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( 11x - 5x - 26 = 28 \)
\( 6x - 26 = 28 \)
Add 26 to both sides:
\( 6x = 28 + 26 \)
\( 6x = 54 \)
Divide by 6:
\( x = \frac{54}{6} = 9 \)

Step4: Find \( PR \)

Substitute \( x = 9 \) into \( PR = 5x + 28 \):
\( PR = 5(9) + 28 = 45 + 28 = 73 \)

Answer:

\( 73 \)