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:

rectangle abcd

Step-by-step explanation:

ae =8cm

ad=5cm

the perimeter of a rectangle = length into breadth

so 8 into 5 = 40

therefore the perimeter of a rectangle is 40

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Answer 2

DE (Radius) = AE + AD = 8 cm + 5 cm = 13 cm

DB = AC = 13 cm (Diagonal of a rectangle are equal)

In right ∆ADC,

AD2 + DC2 = AC2 (By Pythagoras Theorem)

⇒ (5)2 + DC2 = (13)2

⇒ 25 + DC2 = 169

⇒ DC2 = 169 – 25 = 144

⇒ DC = √144 = 12 cm

Perimeter of rectangle ABCD = 2(AD + DC)

= 2(5 cm + 12 cm)

= 2 × 17 cm

= 34 cm