The length and breadth of a rectangle is ^@8 \space cm^@ and ^@15 \space cm^@. Find the radius of the circumcircle of this rectangle.


Answer:

^@8.5 \space cm^@

Step by Step Explanation:
  1. The following figure shows the rectangle ^@ABCD^@ with its circumcircle,

    ^@AB^@ and ^@BC^@ are the length and the breadth of the rectangle ^@ABCD^@ and ^@AC^@ is the diameter of the circumcircle of the rectangle ^@ABCD^@.
    According to the question, ^@AB = 15 \space cm,^@
    ^@ BC = 8 \space cm.^@
  2. ^@\begin{align} \text { Now, in the right-angled triangle } ABC, AC^2 & = AB^2 + BC^2 \\ \implies AC & = \sqrt { AB^2 + BC^2 } \\ & = \sqrt { (15)^2 + (8)^2 } \\ & = 17 \space cm \end{align}^@
  3. The diameter of the circumcircle of the rectangle ^@= 17 \space cm^@.
    The radius of the circumcircle of the rectangle ^@= \dfrac { 17 }{2} = 8.5 \space cm^@.

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