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. Find the cost of levelling the roads at R1.25 per sq m. What is the answer?
Answers
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
CONCEPT :-
- in this question we have discussed the concept of surface area and Volume first of all we will explain with example suppose wehave the cubiod dimensions 21 cm is length 11 is breadth 14 is height we have given that At the rate of 10 rupees per cm² we have paint to do first of allcubiod in which form cuboidal form so, then we have Required surface area to be painted = 2(lb + bh + hl) in Formula L is Length b is breadth h is height we have to do value put up
- 2(21 × 11 + 11 × 14 +14 x 21) we have to solve we get 2(231+ 154 + 294) then, we have bracket quantity to add we get 2 ( 679) we will multiply it we get 1358cm² so, we have get the surfacearea so, we have paint it in which form brick form then, we will write. Now, cost of painting
- = Rs. (1358 x 10) then, we have to multiply it we get so, cost of painting = rs 13580
PROVIDED INFORMATION :-
A rectangular garden is 185 m long and 220 m wide
It has two roads in its centre of
uniform width of 4 m
QUESTION :-
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. Find the cost of levelling the roads at R1.25 per sq m.
TO FIND :-
- Find the cost of levelling the roads at R1.25 per sq m = ?
USING CONCEPT :-
formula to find rectangle area Length × breadth
Formula to find square area = side × side
SOLUTION :-
Let first we have to draw the diagram
you can see in the second attachment file
first diagram is for concept
Area of the road parallel to the length =
185 × 4m = 740m²
Area of the road parallel to the breadth =
220 × 4m = 880m²
Area of the shaded portion = 4 × 4 = 16m²
Area of the roads = ( 740 + 880 - 16 ) m²
= 1,604m²
Cost of levelling the roads atRs 1.25 per sq m 1,604 × 1.25 = 2005
Hence, the cost of levelling the roads
is rs 2005
