The area of a square is 1225 sq. cm whose side is five times of the radius of a circle. The circumference of the circle is equal to the length of the rectangle. If the area of the rectangle is 924 sq. cm, then, find the breadth of the rectangle?

Question

The area of a square is 1225 sq. cm whose side is five times of the radius of a circle. The circumference of the circle is equal to the length of the rectangle. If the area of the rectangle is 924 sq. cm, then, find the breadth of the rectangle?

21 cm
20 cm
25 cm
28 cm
None of these

LohaHridoy

4 views

2025-01-04 04:42

2 Answers

AhmedNazir

Option 1 : 21 cm

Given:

Area of square = 1225 sq. cm

Side of square = 5 × Radius of circle

Perimeter of circle = Length of rectangle

Area of rectangle = 92 sq. cm

Formula Used:

Area of square = Side × Side

Circumference of circle = 2πr

Area of rectangle = length × breadth

Calculation:

The area of the square = 1225 sq. cm

Side of square = √1225

⇒ side of square = 35 cm

∴ Radius of the circle = 35/5 = 7 cm

Perimeter of circle = 2πr = 2 × 22/7 × 7

⇒ 44 cm

So, the length of the rectangle = 44 cm

Area of rectangle = length × breadth

⇒ 924 = 44 × breadth

⇒ breadth = 924/44

⇒ breadth = 21 cm

∴ The breadth of the rectangle is 21 cm.

4 views Answered 2022-09-04 04:29

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 21 cm

Given:

Area of square = 1225 sq. cm

Side of square = 5 × Radius of circle

Perimeter of circle = Length of rectangle

Area of rectangle = 924 sq. cm

Formula Used:

Area of square = Side × Side

Circumference of circle = 2πr

Area of rectangle = length × breadth

Calculation:

The area of the square = 1225 sq. cm

Side of square = √1225

⇒ side of square = 35 cm

∴ Radius of the circle = 35/5 = 7 cm

Perimeter of circle = 2πr = 2 × 22/7 × 7

⇒ 44 cm

So, the length of the rectangle = 44 cm

Area of rectangle = length × breadth

⇒ 924 = 44 × breadth

⇒ breadth = 924/44

⇒ breadth = 21 cm

∴ The breadth of the rectangle is 21 cm.