The figure shows a rectangular field XYZA. Owen walked from X to Y to Z to A and he covered a distance of 72 m. Winnie walked from Y to Z to A to X and she covered a distance of 54 m.
- What is the perimeter of the field?
- Some construction work was undertaken to the same field and a semi-circular part was removed from it. What Is the perimeter of the field after the construction? (Take π = 227)
(a)
Lets assume Length → L and Breadth → B
Owen total covered distance
L + L + B = 72
2 L + B = 72 = A1
Winnie total covered distance
B + L + B = 54
2 B + L = 54 = A2
A1 + A2
3 B + 3 L = 126
B + L = 126 ÷ 3 = 42 m
Perimeter of the field
= 2 (B + L)
= 2 x 42
= 84 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 84 + 11 - 7
= 88 m
Answer(s): (a) 84 m; (b) 88 m