The figure shows a rectangular field ABCD. Mark walked from A to B to C to D and he covered a distance of 75 cm. Cathy walked from B to C to D to A and she covered a distance of 48 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
Mark total covered distance
L + L + B = 75
2 L + B = 75 = A1
Cathy total covered distance
B + L + B = 48
2 B + L = 48 = A2
A1 + A2
3 B + 3 L = 123
B + L = 123 ÷ 3 = 41 cm
Perimeter of the field
= 2 (B + L)
= 2 x 41
= 82 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 82 + 11 - 7
= 86 cm
Answer(s): (a) 82 cm; (b) 86 cm