The figure shows a rectangular field QRST. Zeph walked from Q to R to S to T and he covered a distance of 58 m. Penelope walked from R to S to T to Q and she covered a distance of 47 m.
- 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
Zeph total covered distance
L + L + B = 58
2 L + B = 58 = A1
Penelope total covered distance
B + L + B = 47
2 B + L = 47 = A2
A1 + A2
3 B + 3 L = 105
B + L = 105 ÷ 3 = 35 m
Perimeter of the field
= 2 (B + L)
= 2 x 35
= 70 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 70 + 11 - 7
= 74 m
Answer(s): (a) 70 m; (b) 74 m