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Rectangle ABCD is formed in a circle as shown in the figure. If $AE =8 cm$ and $AD=5 cm$, find the perimeter of the rectangle.

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Given :

In the given figure, $AE =8 cm$ and $AD=5 cm$.

To do :

We have to find the perimeter of the rectangle.

Solution :

In the following figure, 

$AE+AD = DE$ 

$5+8 = 13 cm$

$DE = 13 cm$

DE and DB are the radii of the circle.

So, $DE = DB = 13 cm$.

                        

$BD$ is the diagonal of the rectangle $ABCD$ and the Hypotenuse of the triangle $ABD$.

Therefore, in $\triangle ABD$, 

$AB^2 + AD^2 = BD^2$

$AB^2 + 5^2 + 13^2$

$AB^2 + 25 = 169$

$AB^2 = 169-25$

$AB^2 = 144$

$AB=12 cm$.

So, the length of the rectangle is 12 cm, and the breadth of the rectangle is 5 cm.

The perimeter of the rectangle $ABCD = 2(length+breadth)$

                                                               $ = 2(12+5)$

                                                               $ = 2(17) = 34 cm$.

Therefore, the perimeter of the rectangle $ABCD$ is 34 cm.

                                           

 

Updated on: 10-Oct-2022

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