A wire in the form of a circle of diameter 35cm
is bent to form a rectangle whose length is twice
its breadth. Find the area of the rectangle

Respuesta :

Answer:

[tex]Area=671.7cm^2[/tex]

Step-by-step explanation:

This means that the perimeter of the rectangle formed is equal to the circumference of the circle

[tex]Circumference=\pi d\\\\Circumference=35\pi[/tex]

Let the length of the rectangle be a and the breadth be b.

[tex]a=2b\\\\Perimeter=35\pi \\\\2a+2b=35\pi \\\\2(2b)+2b=35\pi \\\\6b=35\pi \\\\b=\frac{35\pi }{6}\\\\Area=a\times b\\\\Area=2b\times b\\\\Area=2b^2\\\\Area=2\times (\frac{35\pi }{6})^2\\\\Area=671.7cm^2[/tex]

The wire length = 35*pi

Rectangle length = 35/3*pi

Rectangle breadth = 35/6*pi

Answer: Rectangle area = (35/6*pi)(35/3*pi) = 68.05555555555555555554*pi*pi = about 671.00055555555555555543

round to 671