This question was uploaded on 29/09/21 on social media accounts.
A square and a rectangle combined to form another rectangle are inscribed in a circle. A chord of length 5 units is made by extending the diagonal of the square.
Solution 1:
Chord theorem:
\[(a\sqrt2)(5-a\sqrt2)=(a)(b)\]
\[\Rightarrow 2a+b=5\sqrt2\]
Perimeter (ABCD):
\[P = 4a+2b\]
\[\Rightarrow P = 2(5\sqrt2) = 10\sqrt2\]
Solution 2:
Triangle 1 and Triangle 2 are similar:
\[\Rightarrow \frac{5-a\sqrt2}{b}=\frac{a}{a\sqrt2}\]
\[\Rightarrow 2a+b=5\sqrt2\]
Perimeter (ABCD):
\[P = 4a+2b\]
\[\Rightarrow P = 2(5\sqrt2) = 10\sqrt2\]
Solution 3:
The beautiful solution from Twitter:
Puzzle related to Geometry, Square, Rectangle, Length.
