Rectangle ABCD is formed in a circle as shown in Fig. 9.12. If AE = 8 cm and AD = 5 cm, find the perimeter of the rectangle.

Solution:

We know that

DE = EA + AD = (8 + 5)cm =13 cm

From the figure

DE is the radius of the circle

Similarly, DB is the radius of the circle

As the diagonals of a rectangle are equal in length, AC = DB

Hence, AC = 13 cm

From ∆ADC,

DC² = AC² - AD²

Substituting the values

= 13² - 5²

= 169 - 25

= 144

DC² = 12²

DC = 12

So length of DC is 12 cm

Perimeter = 2 (12 + 5)cm = 34 cm

Therefore, the perimeter of the rectangle is 34 cm.

✦ Try This: Circumference of a circle is 11 cm. Find its area.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Sample Problem 14

Rectangle ABCD is formed in a circle as shown in Fig. 9.12. If AE = 8 cm and AD = 5 cm, find the perimeter of the rectangle.

Summary:

Rectangle ABCD is formed in a circle as shown in Fig. 9.12. If AE = 8 cm and AD = 5 cm, the perimeter of the rectangle is 34 cm

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