Question

quadrilateral abcd is a square and the length of \\(\overline{be}\\) is 6 cm. what is the length of \\(\overline{ac}\\)? enter your answer in the box. the length of \\(\overline{ac}\\) = \\(\square\\) cm

Explanation:

Step1: Recall square diagonal properties

In a square, the diagonals are equal in length and bisect each other. So, diagonals \( AC \) and \( BD \) are equal, and \( E \) (the intersection of diagonals) bisects both diagonals. Thus, \( BE = ED \) and \( AE = EC \), and \( AC = BD \).

Step2: Calculate length of \( AC \)

Given \( BE = 6 \) cm. Since \( BD = BE + ED \) and \( BE = ED \) (diagonals bisect each other), \( BD = 6 + 6 = 12 \) cm. And since \( AC = BD \) (diagonals of square are equal), \( AC = 12 \) cm.

Answer:

12