The figure shows a rectangular field TUVW. Lee walked from T to U to V to W and he covered a distance of 55 m. Olivia walked from U to V to W to T and she covered a distance of 53 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
Lee total covered distance
L + L + B = 55
2 L + B = 55 = A1
Olivia total covered distance
B + L + B = 53
2 B + L = 53 = A2
A1 + A2
3 B + 3 L = 108
B + L = 108 ÷ 3 = 36 m
Perimeter of the field
= 2 (B + L)
= 2 x 36
= 72 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 72 + 11 - 7
= 76 m
Answer(s): (a) 72 m; (b) 76 m