The figure shows a rectangular field UVWX. Ryan walked from U to V to W to X and he covered a distance of 71 cm. Xuan walked from V to W to X to U and she covered a distance of 46 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
Ryan total covered distance
L + L + B = 71
2 L + B = 71 = A1
Xuan total covered distance
B + L + B = 46
2 B + L = 46 = A2
A1 + A2
3 B + 3 L = 117
B + L = 117 ÷ 3 = 39 cm
Perimeter of the field
= 2 (B + L)
= 2 x 39
= 78 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 78 + 11 - 7
= 82 cm
Answer(s): (a) 78 cm; (b) 82 cm