The figure shows a rectangular field RSTU. Henry walked from R to S to T to U and he covered a distance of 59 cm. Lucy walked from S to T to U to R and she covered a distance of 49 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
Henry total covered distance
L + L + B = 59
2 L + B = 59 = A1
Lucy total covered distance
B + L + B = 49
2 B + L = 49 = A2
A1 + A2
3 B + 3 L = 108
B + L = 108 ÷ 3 = 36 cm
Perimeter of the field
= 2 (B + L)
= 2 x 36
= 72 cm
(b)
Circumference of the semicircle
=
227 x 7 x
12 = 11 cm
Perimeter of the remaining field
= 72 + 11 - 7
= 76 cm
Answer(s): (a) 72 cm; (b) 76 cm