Question

The door in the diagram is made from a semicircle of radius r and a square with sides
of length 2r. The perimeter of the door is 6.4 m long. Find the width of the door in cm.
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Answer 1

The answer would be 1.4 m

1) The door is made of a  square and a semicircle adjoined on the top.

2) The perimeter of the door would be sum of three sides of square + perimeter of the semicircle

3) Perimeter or Circumference of Semicircle = π r

4) Side of Square =  2r

5) Total Perimeter = 2r + 2r+ 2r +  π r =( 6+ π) r

6) Given Perimeter = 6.4 m

7) Equating both perimeters => ( 6+ π) r = 6.4 m

8) Inserting value of pi => (6+ 3.14) r = 6.4 m

9) r = 0. 7 m

10) Width of door = 2r = 2*0.7 m = 1.4 m