A rectangular garden is 182m long and 222m wide. It has two roads in its centre of uniform width of 4 m, one parallel to its length and the other parallel to its breadth. Find the cost of levelling the roads at R1.26 per sq m. What is the answer?
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Answers
Answer:
Area of rectangular field=l×b=(25×15)=375m
2
Area of 2 path's=(25×2)+(2×15)=80m
2
Area of common square formed at center=2×2=4m
2
Now, area covered by grass=375−(80−4)=375−76
=299m
2
Step-by-step explanation:
Given :-
A rectangular garden is 185 m long and 220 m wide.
It has two roads in its centre of uniform width of
4 m
One parallel to its length and the other parallel to its breadth.
To find :-
The cost of levelling the roads at Rs.1.25 per sq m.
Solution :-
Given that
The length of the rectangular garden
(l) = 185 m
The width of the rectangular garden
(b) = 225 m
Width of the road (w) = 4 m
On converting the above data into pictorial representation then we have,
AB = CD = EF = GH = 185 m
AD = BC = PR = QS = 220 m
EG = FH = RS = PQ = 4 m
We know that
Area of a rectangle = length×breadth sq.units
Area of the rectangle EFGH
= EF × FH
= 185 × 4
= 740 m²
Area of the rectangle PQRS
= PR×PQ
= 220×4
= 880 m²
We know that
Area of a square =side × side sq.units
Area of the square KLMN
= KL × KN
= 4×4
= 16 m²
Area of the roads = Area of EFGH + Area of PQRS - Area of KLMN
=> Area of the roads = 740+880-16
=> Area of the roads = 1620-16
Area of the roads = 1604 m²
The cost of levelling the roads per 1 m²
= Rs. 1.25
The cost of levelling the roads of 1616 m²
= 1604×1.25
= Rs. 2005
Alternative Method :-
.
We have,
Length = 185 m
Width = 220 m
Width of the road = 4 m
l = 185 m
b = 220 m
w = 4 m
The Area of the roads = (l+b-w)w sq.units
=> (185+220-4)4 m²
=> (405-4)4 m²
=> (401)(4) m²
=> 1604 m²
Area of the roads = 1604 m²
The cost of levelling the roads per 1 m²
= Rs. 1.25
The cost of levelling the roads of 1616 m²
= 1604×1.25
= Rs. 2005
Answer :-
The total cost of levelling the roads is Rs. 2005
Used formulae:-
→ Area of a rectangle = length×breadth sq.units
→ Area of a square =side × side sq.units
