Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem11

Levels 9&10 Video Solutions 2010 problem11

Video Transcription

Video Summary

The problem involves finding the length of segment \( F, E \) in a geometric figure including a square \( A, B, C, D \) with side length 1 and two equilateral triangles, \( B, C, F \) and \( C, E, D \). Since all sides of the square and triangles measure 1, the triangles form a right triangle \( F, C, E \) with angle measurements confirming this. Using the Pythagorean theorem, the formula \( x^2 = 1^2 + 1^2 \) indicates \( x \) equals the square root of 2. Therefore, the length of segment \( F, E \) is \(\sqrt{2}\), corresponding to answer A.

Keywords

geometry

square

equilateral triangle

Pythagorean theorem

segment length