The length of a rectangle is 6 cm more than its breadth andits perimeter is 100 cm.If the area of the
rectangle is very nearly equal to the area of a circle, then whatis the circumference of the circle?
Answers
Answer:
88cm
Step-by-step explanation:
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Quantitative Aptitude ≫ Mensuration ≫ Plane Figures
Question:
The length of a rectangle is 6cm more than its breadth and its perimeter is 100 cm. If the area of the rectangle is very nearly equal to the area of a circle, then what is the circumference of the circle?(Take π = 22/7)
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Options:
132 cm
66 cm
88 cm
110 cm
Correct Answer: Option 3 (Solution Below)
Solution:
Let the breadth of the rectangle be x cm
Length of the rectangle = (x + 6) cm
As we know,
Perimter of the rectangle = 2 (l + b)
2 (l + b) = 100
⇒ 2 (x + 6 + x) = 100
⇒ 2x + 6 = 100/2
⇒ 2x + 6 = 50
⇒ 2x = 50 – 6
⇒ 2x = 44
⇒ x = 44/2
⇒ x = 22
Breadth of the rectangle = 22 cm
Length of the rectangle = 22 + 6 = 28 cm
Area of the rectagel = 28 × 22
Given,
Area of circle = Area of the rectangle
πr2 = 28 × 22
⇒ (22/7) × r2 = 28 × 22
⇒ r2 = 28 × 4
⇒ r = √[7 × 7 × 2 × 2]
⇒ r = 14
Circumference of the circle = 2πr = 2 × (22/7) × 14 = 88 cm
Answer:
L- 28cm
B- 22cm
Step-by-step explanation:
let the length be x+6 and breadth be x
2(l+b) = 100cm
2(x+6+x) =100
2x+12+2x=100
4x+12=100
4x=100-12
4x=88
x= 22
length- 28cm(x+6)
breadth- 22cm