Question

A circle circumscribes a rectangle whose sides are in the ratio 4 : 3. If the perimeter of the rectangle is 56 cm, then what is the area of the circle ?
Options:

1. 90 π
2. 70 π
3. 96 π
4. 100 π​

Answer 1

Gɪᴠᴇɴ :-

• Sides Ratio of Rectangle = 4 : 3.
• Perimeter of Rectangle = 56cm.

Tᴏ Fɪɴᴅ :-

• Area of circumscribes circle ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Perimeter of Rectangle = 2(Length + Breadth).
• Diagonal of Rectangle = √[(Length)² + (Breadth)²]
• Radius = (Diameter)/2
• Area of circle = π * (Radius)².
• when a circle is drawn outside a rectangle , Diameter of circle is Equal to Diagonal of Rectangle.

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Length & Breadth of Rectangle are 4x & 3x.

Than,

→ 2(4x + 3x) = 56 = Perimeter

→ 2 * 7x = 56

→ 7x = 28

→ x = 4 cm.

So,

→ Length = 4*4 = 16cm.

→ Breadth = 4*3 = 12cm.

Therefore,

→ Diagonal of Rectangle = √(16² + 12²) = √(256 + 144) = √400 = 20cm.

So,

→ Diameter of circumscribes circle = Diagonal of Rectangle = 20cm.

Than,

→ Radius of circle = (20/2) = 10cm.

Hence,

→ Area of circumscribes circle = π * (10)² = 100π (Option 4) (Ans.)

ஃ Area of circle will be 100π.

Answer 2

Let the side be 4x and 3x

perimeter of rectangle =2(l+b)

56 = 2(4x+3x)

56 = 14x

x = 56/14 =4

x =4

4x = 4×4 =16

3x = 3×4 =12

Circumference of circle = perimeter of rectangle

2 × pi × r = 2(l+b)

r = 2(16+12)÷(2×3.14)

r = 8.91cm

Area of circle = pi × r²

= 3.14 ×(8.91×8.91)

= 249.27 cm²