The figure shows a rectangular field TUVW. Gabriel walked from T to U to V to W and he covered a distance of 65 m. Tiffany walked from U to V to W to T and she covered a distance of 46 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
Gabriel total covered distance
L + L + B = 65
2 L + B = 65 = A1
Tiffany total covered distance
B + L + B = 46
2 B + L = 46 = A2
A1 + A2
3 B + 3 L = 111
B + L = 111 ÷ 3 = 37 m
Perimeter of the field
= 2 (B + L)
= 2 x 37
= 74 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 74 + 11 - 7
= 78 m
Answer(s): (a) 74 m; (b) 78 m