The figure shows a rectangular field MNPQ. Fred walked from M to N to P to Q and he covered a distance of 56 m. Marion walked from N to P to Q to M and she covered a distance of 40 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
Fred total covered distance
L + L + B = 56
2 L + B = 56 = A1
Marion total covered distance
B + L + B = 40
2 B + L = 40 = A2
A1 + A2
3 B + 3 L = 96
B + L = 96 ÷ 3 = 32 m
Perimeter of the field
= 2 (B + L)
= 2 x 32
= 64 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 64 + 11 - 7
= 68 m
Answer(s): (a) 64 m; (b) 68 m