Question

quadrilateral bcde is an isosceles trapezoid, $bd = a + 97$, and $ce = 2a + 25$. what is the value of $a$?
$a = \square$

Explanation:

Step1: Recall property of isosceles trapezoid

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

Step2: Set up the equation

Given \( BD = a + 97 \) and \( CE = 2a + 25 \), we set them equal: \( a + 97 = 2a + 25 \).

Step3: Solve for \( a \)

Subtract \( a \) from both sides: \( 97 = a + 25 \).
Then subtract 25 from both sides: \( a = 97 - 25 = 72 \).

Answer:

\( 72 \)