The radius of a circle is equal to length of the rectangle. The circumference of the circle and breadth of the rectangle is 132 cm and 20 cm respectively. The diagonal of the rectangle is:(Take $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 2
We know that,
Circumference of the rectangle = 2πr
Diagonal of rectangle = (length)2 + (breadth)2
Given,
Circumference = 132 cm
Breadth = 20 cm
So, 2 πr = 132
= 2 × \(\frac{22}{7}\)× r = 132
= r = 132 × \(\frac{7}{22}\)× \(\frac{1}{2}\) = 21 cm
We know the length = radius
Then, diagonal of the rectangle
= d2 = l2 + b2
= d2 = 212 + 202
= d2 = 441 + 400
= d = \(\sqrt {841}\) = 29 cm