Theory question 111
Mensuration of Plane Shapes(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take π = 22/7]
(b) A rope 60 cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the (i) length; (ii) diagonal of the rectangle.
Show the model answer
Model answer
(a) The square's side is 2r. 8r + 2 × 22/7 × r = 100 → r(56 + 44)/7 = 100 → r = 7 cm.
(b) 2(l + b) = 60 and l = 4b → 10b = 60 → b = 6 cm.
(i) l = 24.0 cm.
(ii) Diagonal = √(242 + 62) = √612 ≈ 24.7 cm.
Explanation
A circle inscribed in a square has diameter equal to the side of the square.