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In rectangle ABCD, parallel lines k and m through A and C are perpendicular to diagonal BD and divide it into three equal segments of 1. What is the area of rectangle ABCD?

 May 28, 2021
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In rectangle ABCD, parallel lines k and m through A and C are perpendicular to diagonal BD and divide it into three equal segments of 1. What is the area of rectangle ABCD?

 

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\(y^2-1^2=x^2-2^2\\ x^2+y^2=3^2\)

\(y^2=\\ x^2-2^2+1^2=3^2-x^2\\ 2x^2=3^2+2^2-1^2\\ x^2=12/2\\ x=\sqrt{6}\\ y^2=9-x^2\\ y^2=9-6\\ y=\sqrt{3}\)

\(A_{ABCD}=\sqrt{3\cdot 6}\)

\(A_{ABCD}=3\cdot \sqrt{2}\)

 May 28, 2021
edited by asinus  May 28, 2021

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