Question

quadrilateral qrst is an isosceles trapezoid, $qs = 3b - 82$, and $rt = 2b$. what is the value of $b$?
$b = \square$

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal in length. So, \( QS = RT \).

Step2: Set up the equation

Given \( QS = 3b - 82 \) and \( RT = 2b \), we set them equal: \( 3b - 82 = 2b \).

Step3: Solve for \( b \)

Subtract \( 2b \) from both sides: \( 3b - 2b - 82 = 2b - 2b \), which simplifies to \( b - 82 = 0 \). Then add 82 to both sides: \( b - 82 + 82 = 0 + 82 \), so \( b = 82 \).

Answer:

\( 82 \)