Question

1. if abcd is a square and ac = 26, find bc.

Explanation:

Step1: Define side length

Let side \( BC = x \). Diagonal \( AC = 20 \).

Step2: Apply Pythagorean theorem

In square, \( AC^2 = AB^2 + BC^2 = x^2 + x^2 = 2x^2 \).

Step3: Solve for x

\( 20^2 = 2x^2 \Rightarrow 400 = 2x^2 \Rightarrow x^2 = 200 \Rightarrow x = 10\sqrt{2} \).

Answer:

\( 10\sqrt{2} \)