The diameter of the circumcircle of a rectangle is ^@13 \space c | Math Question and Answer | Edugain Qatar

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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:

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 $12 \space cm$ .

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