Question

quadrilateral qrst is a rectangle, qs = 3z, and rt = z + 92. what is qs?

Explanation:

Step1: Recall rectangle diagonals property

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

Step2: Set up the equation

Given \( QS = 3z \) and \( RT = z + 92 \), we set \( 3z = z + 92 \).

Step3: Solve for \( z \)

Subtract \( z \) from both sides: \( 3z - z = 92 \), which simplifies to \( 2z = 92 \). Then divide both sides by 2: \( z=\frac{92}{2}=46 \).

Step4: Find \( QS \)

Substitute \( z = 46 \) into \( QS = 3z \): \( QS = 3\times46 = 138 \).

Answer:

\( 138 \)