The figure shows a rectangular field XYZA. Xavier walked from X to Y to Z to A and he covered a distance of 56 cm. Emily walked from Y to Z to A to X and she covered a distance of 43 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
Xavier total covered distance
L + L + B = 56
2 L + B = 56 = A1
Emily total covered distance
B + L + B = 43
2 B + L = 43 = A2
A1 + A2
3 B + 3 L = 99
B + L = 99 ÷ 3 = 33 cm
Perimeter of the field
= 2 (B + L)
= 2 x 33
= 66 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 66 + 11 - 7
= 70 cm
Answer(s): (a) 66 cm; (b) 70 cm