question_answer

Rectangle ABCD is formed in a circle as shown. If AE = 8 cm and AD = 5 cm, find the perimeter of the rectangle.    

Answer:

DE - EA + AD - (8 + 5) cm - 13 cm DE is the radius of the circle. Also, DB is the radius of the circle.                  Next, AC == DB [Since diagonals of a rectangle are equal in length] Therefore,     AC = 13 cm. From\[\Delta ADC,\text{ }D{{C}^{2}}\text{ }=A{{C}^{2}}-A{{D}^{2}}-{{13}^{2}}-{{5}^{2}}\]                \[=169-25=144-{{12}^{2}}\] So,             DC = 12 cm Thus, length of DC is 12 cm. Hence, perimeter of the rectangle ABCD =2(12 + 5) cm - 34 cm.