Page 271 - Start Up Mathematics_8 (Non CCE)

Solution: Area of the square plot = 25 m × 25 m = 625 m 2
Area of the plot where house is to be constructed

= 20 m × 15 m = 300 m 2
Area of the garden = Area of square plot – Area of the plot where house is to be constructed
2
= (625 – 300) m = 325 m 2
2
Cost of developing 1 m garden = ` 55
2
\ Cost of developing 325 m garden = ` (325 × 55) = ` 17,875
2
Example 8: The area of a rhombus is 252 cm . If one of the diagonals measures 18 cm, find the length
of the other diagonal.
Solution: Area of rhombus = 252 cm 2
Length of the diagonal (d ) = 18 cm
1
Let the length of the second diagonal be d cm.
2
1
Now, area of rhombus = × d × d
2 1 2
1 2 252¥
fi 252 = × 18 × d fi d = = 28 cm
2 2 2 18
Length of the other diagonal = 28 cm
Example 9: There are 3 different shaped paths in a big lawn. Renu who goes for a walk in the lawn, walks
along all the three paths. On which path does she have to walk the least? (NCERT)
K

T S 2.4 m
V 2.4 m

2 m L N
Q
U W P R M
3.4 m 3.4 m 3.4 m
(a) (b) (c)

Solution: (a) Diameter UW = 3.4 m
34.
fi Radius (r) = = 1.7 m
2
Perimeter of the path = pr + 2r = 22 × 1.7 + 2 × 1.7
7
= 5.34 + 3.4 = 8.74 m

(b) Perimeter of the path = PT + TS + SR + PQR

Ê 34. ˆ 22
= 2 + 3.4 + 2 + p × Á Ë 2 ¯ = 7.4 + 7 × 1.7
˜
= 7.4 + 5.34 = 12.74 m


(c) Perimeter of the path = KL + LMN + KN
Ê 34. ˆ 22
= 2.4 + Á 2 ¯ + 2.4 = 2.4 + 7 × 1.7 + 2.4
˜
Ë
= 4.8 + 5.34 = 10.14 m
\ Renu has to walk the least in path UVW.

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