The figure shows a rectangular field NPQR. Archie walked from N to P to Q to R and he covered a distance of 62 m. Ivory walked from P to Q to R to N and she covered a distance of 52 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
Archie total covered distance
L + L + B = 62
2 L + B = 62 = A1
Ivory total covered distance
B + L + B = 52
2 B + L = 52 = A2
A1 + A2
3 B + 3 L = 114
B + L = 114 ÷ 3 = 38 m
Perimeter of the field
= 2 (B + L)
= 2 x 38
= 76 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 76 + 11 - 7
= 80 m
Answer(s): (a) 76 m; (b) 80 m