The figure shows a rectangular field PQRS. Wesley walked from P to Q to R to S and he covered a distance of 78 m. Vanessa walked from Q to R to S to P and she covered a distance of 51 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
Wesley total covered distance
L + L + B = 78
2 L + B = 78 = A1
Vanessa total covered distance
B + L + B = 51
2 B + L = 51 = A2
A1 + A2
3 B + 3 L = 129
B + L = 129 ÷ 3 = 43 m
Perimeter of the field
= 2 (B + L)
= 2 x 43
= 86 m
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 m
Perimeter of the remaining field
= 86 + 11 - 7
= 90 m
Answer(s): (a) 86 m; (b) 90 m