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^@

Step by Step Explanation:
  1. 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^@.
  2. ^@\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}^@
  3. Hence, the length of the rectangle is ^@12 \space cm^@.

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