The figure shows a rectangular field YZAB. Carl walked from Y to Z to A to B and he covered a distance of 67 cm. Lynn walked from Z to A to B to Y and she covered a distance of 44 cm.
- 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
Carl total covered distance
L + L + B = 67
2 L + B = 67 = A1
Lynn total covered distance
B + L + B = 44
2 B + L = 44 = A2
A1 + A2
3 B + 3 L = 111
B + L = 111 ÷ 3 = 37 cm
Perimeter of the field
= 2 (B + L)
= 2 x 37
= 74 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 74 + 11 - 7
= 78 cm
Answer(s): (a) 74 cm; (b) 78 cm