Geometry Problem
Click the figure below to see the complete problem 517 about Right Triangle, Six Squares, Areas.
See also:
Complete Problem 517
Level: High School, SAT Prep, College geometry
Tuesday, August 31, 2010
Problem 517: Right Triangle, Six Squares, Areas
See also:
Complete Problem 517
Level: High School, SAT Prep, College geometry
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name AB = a, BC = b, AC = c
ReplyDeleteS1 + S2 + S3 = a² + b² + (a² + b²) = 2a² + 2b²
extend BA,it meet side of A5 in midpoint
Str on the right of A5 is (a∙b)/2 =>
Str/2 = (a∙b)/4 =>
side of A5 = 4a² + b²
Str on the left of A6 is a² + 4b²
S5 + S4 + S6 = (4a + b²) + (a² + b²) + (a² + 4b²)
= 6a² + 6b²
In general, 3x(A4+A1+A2)=A3+A5+A6.
ReplyDeleteWhen triangle ABC is a right triangle, A3=A4.
So, 3x(A1+A2+A3)=A4+A5+A6.