The figure shows a rectangular field PQRS. Andy walked from P to Q to R to S and he covered a distance of 70 cm. Barbara walked from Q to R to S to P and she covered a distance of 53 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
Andy total covered distance
L + L + B = 70
2 L + B = 70 = A1
Barbara total covered distance
B + L + B = 53
2 B + L = 53 = 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