Through a rectangular field of length 90m and breadth 60m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3m, Find:
(i) the area covered by the roads
(ii) the cost of constructing the roads at the rate of ₹110 per m²
Answers
Step by step Explanation:-
Given:-
- Length of Rectangular field = 90m
- Breadth of Rectangular field = 60m
- Width of road at centre = 3m
Need To Find:-
- Area of Roads
- cost of constructing the roads at the rate of ₹110 per m²
Where:-
- L denotes Length
- B denotes Breadth
Explanation:-
[Take a look at Attachment] In this Question, We are provided with the length of Rectangular field that is 90m and Breadth that is 60m and there is small road at centre of Rectangular field of 3m that is cuts at right angles through centre of fields
Solution:-
PQ = 3m ; QR = 60m
EF = 90m ; FG = 3m
KL = 3m
⠀⠀
Area of Rectangular Road = QR × PQ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 60 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 180m²
⠀⠀
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Now, We have to find the area Rectangular road EFGH.
Area of Rectangular road EFGH = L × B
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 90 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 270m²
⠀⠀
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Now, we have to find the area of Square KLMN between Rectangular road
Area of Square KLMN = Side × Side
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 9m²
⠀⠀
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Now, Let's find the Area of Roads ATQ.
(i) Area of Roads = Area of PQRS + Area EFGH - Area of KLMN
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 180 + 270 - 9
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 450 - 9
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 441m²
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(ii) Cost of Constructing at 1m² = ₹110
⠀⠀Cost of Constructing at 441m² = 110 × 441
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ₹48,510
⠀⠀
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Step by step Explanation:-
Given:-
Length of Rectangular field = 90m
Breadth of Rectangular field = 60m
Width of road at centre = 3m
Need To Find:-
Area of Roads
cost of constructing the roads at the rate of ₹110 per m²
Where:-
L denotes Length
B denotes Breadth
Explanation:-
[Take a look at Attachment] In this Question, We are provided with the length of Rectangular field that is 90m and Breadth that is 60m and there is small road at centre of Rectangular field of 3m that is cuts at right angles through centre of fields
Solution:-
PQ = 3m ; QR = 60m
EF = 90m ; FG = 3m
KL = 3m
⠀⠀
Area of Rectangular Road = QR × PQ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 60 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 180m²
\therefore{\underline{\sf{\orange{Hence, \: Area \: of \: Rectangular \: road \: is \: {180m}^{2}}}}}∴Hence,AreaofRectangularroadis180m2
⠀⠀
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Now, We have to find the area Rectangular road EFGH.
Area of Rectangular road EFGH = L × B
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 90 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 270m²
\therefore{\underline{\sf{\orange{Hence, \: Area \: of \: Rectangular \: road \: is \: {270m}^{2}}}}}∴Hence,AreaofRectangularroadis270m2
⠀⠀
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Now, we have to find the area of Square KLMN between Rectangular road
Area of Square KLMN = Side × Side
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3 × 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 9m²
\therefore{\underline{\sf{\orange{Hence, \: Area \: of \: Square \: is \: {9m}^{2}}}}}∴Hence,AreaofSquareis9m2
⠀⠀
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Now, Let's find the Area of Roads ATQ.
(i) Area of Roads = Area of PQRS + Area EFGH - Area of KLMN
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 180 + 270 - 9
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 450 - 9
⠀⠀⠀⠀⠀⠀⠀⠀⠀= 441m²
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(ii) Cost of Constructing at 1m² = ₹110
⠀⠀Cost of Constructing at 441m² = 110 × 441
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ₹48,510
\therefore{\underline{\sf{\orange{Hence, \:Cost~ of~ Constructing~ is~ Rs. 48,510~}}}}∴Hence,Cost of Constructing is Rs.48,510
⠀⠀
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