Question

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

Answer 1

Answer:

Hii,

Step-by-step explanation:

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DE = EA + AD = (8 + 5)cm =13 cm DE is the radius of the circle. Also, DB is the radius of the circle.

Next, AC = DB [Since diagonals of a rectangle are equal in length]

Therefore, AC = 13 cm.

From ∆ADC, DC2 = AC2 – AD2 = 132 – 52 = 169 – 25 = 144 = 122 So, DC = 12

Thus, length of DC is 12 cm. Hence, perimeter of the rectangle ABCD = 2 (12 + 5)cm = 34.

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Answer 2

Answer:

Given,

• AD = 5cm
• AE = 8cm

${ \sf{ \color{maroon}{Radius \: DE= }}}$ AD + AE

$\begin{gathered}:\implies\sf{ 5 + 8}\\ \\ \\ :\implies\sf{ 13 cm }\end{gathered}$

We know, Length Of Diagonal Of Rectangle = Radius Of circle

${ \sf{ \color{Blue}{Diagonal = }}}$ 13cm

• By applying Pythagoras theoram :-

AC² = AD² + DC²

$\begin{gathered}:\implies\sf{ 13² = 5² + DC²}\\ \\ \\ :\implies\sf{ 169 = 25 + DC }\\ \\ \\ :\implies\sf{ DC = 169 - 25}\\ \\ \\ :\implies\sf{ DC = √144} \\ \\ \\ :\implies\sf{ DC = 12\: cm }\end{gathered}$

${ \sf{ \color{maroon}{Perimeter Of Rectangle = }}}$ 2( l + b )

$\begin{gathered}:\implies\sf{ 2 ( 12 + 5 )}\\ \\ \\ :\implies\sf{ 2 ( 17)}\\ \\ \\ :\implies\sf{ 34 \: cm }\end{gathered}$

Therefore, Perimeter Of given Rectangle Is 34 cm ! :)