Questions: 그림의 A B C D 에 대하여 물음에 답하시오. 【유형1. 직각삼각형의 변의 길이 124. A B C D 의 둘레의 길이는? (1) 12+4√6 (2) 14+4√3 (3) 14+6√3 (4) 12+6√6 (5) 12+8√6 125. A B C D 의 넓이는? (1) 10+4√3 (2) 12+4√6 (3) 12+8√3 (4) 10+8√6 (5) 24+16√3

Solution Steps

• The quadrilateral \(ABCD\) has angles \( \angle DAB = 45^\circ \) and \( \angle BCD = 30^\circ \).
• \(BC = 8\).

• Since \( \angle DAB = 45^\circ \), triangle \(ABD\) is a 45-45-90 triangle.
• In a 45-45-90 triangle, the legs are equal, and the hypotenuse is \( \sqrt{2} \) times the length of each leg.
• Let \(AB = x\). Then \(AD = x\) and \(BD = x\sqrt{2}\).

• Since \( \angle BCD = 30^\circ \), triangle \(BCD\) is a 30-60-90 triangle.
• In a 30-60-90 triangle, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is \( \sqrt{3} \) times the shorter leg.
• Given \(BC = 8\), the hypotenuse \(BD = 8\sqrt{3}\).

Final Answer