Quadrilateral ABCD is a square. Let a, b, c be parallel lines passing through A, B, C, respectively. The distance between lines a and b is 12, and the distance between lines b and c is 17. Find the area of square ABCD.
+26367 Quadrilateral ABCD is a square. Let a, b, c be parallel lines passing through A, B, C, respectively.
The distance between lines a and b is 12, and the distance between lines b and c is 17.
Find the area of square ABCD.
\(\begin{array}{|lrcll|} \hline (1) & \mathbf{\sin(\varphi)} &=& \mathbf{\dfrac{12}{x}} \\\\ (2) & \mathbf{\cos(\varphi)} &=& \mathbf{\dfrac{17}{x}} \\ \hline & \mathbf{\sin^2(\varphi)+\cos^2(\varphi)} &=& \mathbf{1} \\\\ & \left(\dfrac{12}{x}\right)^2+\left(\dfrac{17}{x}\right)^2 &=& 1 \\\\ & \dfrac{144}{x^2}+\dfrac{289}{x^2} &=& 1 \quad | \quad \cdot x^2 \\\\ & 144+289 &=& x^2 \\ & 433 &=& x^2 \\ & \mathbf{x^2} &=& \mathbf{433} \\ \hline \end{array}\)
The area of square ABCD is 433
