Question

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-

(1)The area covered by the roads.

(2)The cost of constructing the roads at the rate of Rs110 per m

Answer 1

Answer:

(1) 441m^2.

(2) Rs 48,510.

Step-by-step explanation:

(1) Here, PQ = 3 m and PS = 60 m, EH = 3 m and EF = 90 m and KL = 3 m and KN = 3 m

Area of roads = Area of PQRS + Area of EFGH – Area of KLMN

[∵ KLMN is taken twice, which is to besubtracted] = PS x PQ + EF x EH – KL x KN

= (60 x 3) + (90 x 3) – (3 x 3)

= 180 + 270 – 9

= 441 m2

(2) The cost of 1 m2 constructing the roads

= Rs 110 The cost of 441 m2 constructing the

roads

=Rs 110 x 441 =Rs 48,510

Therefore, the cost of constructing the roads

= Rs 48,510

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Answer 2

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

Hence, Area of Rectangular road is 180m2

∴Hence,AreaofRectangularroadis180m2

⠀⠀

_____________________________________

Now, We have to find the area Rectangular road EFGH.

Area of Rectangular road EFGH = L × B

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 90 × 3

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 270m²

Hence, Area of Rectangular road is 270m^2

∴Hence,AreaofRectangularroadis270m2