Saturday, June 20, 2009

Problem 306: Square, Triangles, Angle, Side

Proposed Problem
Click the figure below to see the complete problem 306.

 Problem 306: Square, Triangles, Angle, Side.
See also:
Complete Problem 306
Collection of Geometry Problems

Level: High School, SAT Prep, College geometry

2 comments:

  1. From triangle BCE, x^2 = b^2 + BC^2. Now triangles BCE & FAB are similar; hence, a/AB =BC/b or BC^2 = ab since AB=BC. Thus, x^2 = b^2 +ab. QED.

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  2. Let length of square ABCD be y
    Triangle BCE ~ Triangle FDE
    BC/CE=FD/DE
    y/b=FD/(y-b)
    FD=y(y-b)/b
    AF=AD+DF
    a=y+y(y-b)/b=y^2/b
    y^2=ab
    x^2=y^2+b^2=ab+b^2

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