A circular copper wire of radius 7cm is bend to form a rectangle. If the breadth and the length of the rectangle are in the 4:7 respectively. What is the breadth of the rectangle?
let the sides be 4x and 7x
8x + 14x = 7
22x = 7
x = 7/22
then 4x = 4(7/22) = 14/11 cm
To find the breadth of the rectangle formed from the circular copper wire, we can start by finding the length of the wire.
The length of the wire is the circumference of the circle formed by the wire. The formula for the circumference of a circle is given by: C = 2πr, where C is the circumference and r is the radius.
Given that the radius of the circle is 7 cm, we can calculate the circumference using the formula:
C = 2π(7) = 14π cm.
Now, let's assume the breadth of the rectangle is 4x, and the length is 7x, where x is a common multiplier to maintain the ratio of 4:7.
The length of the rectangle will be equal to the total length of the wire:
14π cm = 7x + 7x + 4x + 4x
14π cm = 14x + 8x
14π cm = 22x
Dividing both sides of the equation by 22, we get:
π cm = x
Now, we know that the breadth of the rectangle is 4x, substituting the value of x we found earlier, we can find the breadth:
Breadth = 4(π) = 4π cm.
Therefore, the breadth of the rectangle formed from the circular copper wire is 4π cm.