# Math

A circular copper wire of radius 7cm is bent to form a rectangle. If the breadth and the length of the rectangle are in the ratio 4:7 respectively. What is the breadth of the rectangle?

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1. Given:
radius=7cm
Circumference=perimeter of rectangle
Ratio of breadth:length = 4:7

Let b=breadth,
then length=(7/4)b
circumference=2π(7)=14π
circumference=perimeter
therefore
14π=2(b+(7/4)b)
14&;i;=2(1+7/4)b
(11/2)b=14π
b=14π(5/11)=7.997=8 cm approx.

Check:
perimeter=2(8+(7/4)8)=44 cm
circumference = 14π=43.98=44 cm approx. .......good!

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2. A path that is 2 feet wide surrounds the pond.

What is the combined area of the pond and the path?.

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