Italy
The diameter of the circumcircle of a rectangle is ^@13 \space cm^@ and rectangle's width is ^@5 \space cm^@. Find the length of the rectangle.
Answer:
^@12 \space cm^@
- The following figure shows the rectangle ^@ABCD^@ with its circumcircle,
^@AB, BC, ^@ and ^@AC^@ are the length, breadth, and diameter of the circumcircle of the rectangle ^@ABCD^@.
According to the question, ^@AC = 13 \space cm,^@
^@BC = AD = 5 \space cm^@. - ^@\begin{align} \text { Now, in the right-angled triangle } ABC, AB^2 & = AC^2 - BC^2 \\ \implies AB & = \sqrt { AC^2 - BC^2 } \\ & = \sqrt { (13)^2 - (5)^2 } \\ & = 12 \space cm \end{align}^@
- Hence, the length of the rectangle is ^@12 \space cm^@.
