The figure shows a rectangular field TUVW. John walked from T to U to V to W and he covered a distance of 75 cm. Yen walked from U to V to W to T and she covered a distance of 39 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
John total covered distance
L + L + B = 75
2 L + B = 75 = A1
Yen total covered distance
B + L + B = 39
2 B + L = 39 = A2
A1 + A2
3 B + 3 L = 114
B + L = 114 ÷ 3 = 38 cm
Perimeter of the field
= 2 (B + L)
= 2 x 38
= 76 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 76 + 11 - 7
= 80 cm
Answer(s): (a) 76 cm; (b) 80 cm