Question

pqrs is a rectangle. find the value of x and the length of each diagonal.
pr = 10x - 4 and sq = 7x + 5
x =
pr = sq =

Explanation:

Step1: Recall property of rectangle diagonals

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

Step2: Set up the equation

Given \( PR = 10x - 4 \) and \( SQ = 7x + 5 \), we set them equal:
\( 10x - 4 = 7x + 5 \)

Step3: Solve for \( x \)

Subtract \( 7x \) from both sides: \( 10x - 7x - 4 = 5 \)
Simplify: \( 3x - 4 = 5 \)
Add 4 to both sides: \( 3x = 5 + 4 \)
\( 3x = 9 \)
Divide by 3: \( x = \frac{9}{3} = 3 \)

Step4: Find length of diagonals

Substitute \( x = 3 \) into \( PR \): \( PR = 10(3) - 4 = 30 - 4 = 26 \)
Since \( PR = SQ \), \( SQ = 26 \) too.

Answer:

\( x = 3 \), \( PR = SQ = 26 \)