The diameter of the circumcircle of a rectangle is 13 cm13 cm13 cm and rectangle's width is 5 cm5 cm5 cm. Find the length of the rectangle.
Answer:
12 cm12 cm
- The following figure shows the rectangle ABCDABCD with its circumcircle,
AB,BC,AB,BC, and ACAC are the length, breadth, and diameter of the circumcircle of the rectangle ABCDABCD.
According to the question, AC=13 cm,AC=13 cm,
BC=AD=5 cmBC=AD=5 cm. - Now, in the right-angled triangle ABC,AB2=AC2−BC2⟹AB=√AC2−BC2=√(13)2−(5)2=12 cm
- Hence, the length of the rectangle is 12 cm.