Question

A rectangular garden is 120m long and
80m wide. It has two roads, each 5m wide,

running in the middle

of it, one parallel to its length and the other
parallel to its breadth. Find the cost of
constructing the roads at

120 per m sq


​

Answer 1

$\large\underline{\green{\sf \red{\bigstar} Given:-}}$

• The length of a rectangular garden is 120m long.
• The width (breadth) of the rectangular garden is 80m
• Two roads having width 5m running parallel to length and breadth.

$\large\underline{\purple{\sf \orange{\bigstar} To Find:-}}$

• The cost of constructing the road at Rs. 120 per m sq.

• For this, we have to find the area of the roads.
• By naming different points.

We get two roads,

• Road BCGH,
• Length (l) = 80m
• Breadth (b) = 5m
• Area = l*b
•         = 80 * 5
•         = 400 m sq.

Also,

• Road EFIJ,
• Length (l') = 120m
• Breadth (b') = 5m
• Area = l*b
•         = 120 * 5

        = 600 m sq.

Now,

• Both the roads are intersecting so the area of PQRS is occurring two times.
• Thus, we have to subtract its area once.
• Each side of PQRS square is 5m,
• Area of PQRS = (side)²
•                        = (5)²
•                        = 25 m sq.

Now,

• The area of the road to be constructed is,
• = (Area of BCGH + Area of EFIJ) - Area of PQRS
• = 400 + 600 - 25
• = 1000 - 25
• = 975 m sq.

Now,

• The cost of constructing the road for 1 m sq is Rs. 120
• The cost for constructing the road for 975 m sq, will be
• = 975 * 120
• = Rs. 117000

Hence,

$\large\underline{\pink{\sf \orange{\bigstar}The\:\: total \:\: cost\:\: will \:\: be \:\: 117000.}}$

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$\large\underline{\blue{\sf \red{\bigstar} Note:-}}$

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• $\large\underline{\pink{\sf \orange{\bigstar} Diagram\:\: is\:\: in \:\:attachment}}$

Answer 2

Question Given :

• A rectangular garden is 120m long and 80m wide. It has two roads, each 5m wide, running in the middle of it, one parallel to its length and the other parallel to its breadth. Find the cost of constructing the roads at 120 per m sq

Given parameters :

• The length of a rectangular garden is 120m long.
• The breadth of the rectangular garden is 80m
• Two roads having width 5m running parallel to length and breadth.

To find :

• The cost of constructing the road at Rs. 120 per m sq.

Required solution :

In order to find the cost of constructing the roads we need to find their area first ,

If we name the different points

We get two roads,

Road BCGH,

Length (l) = 80m

Breadth (b) = 5m

Area = length × breadth

= 80 × 5

= 400 m²

Also, in road EFIJ,

Length (l') = 120m

Breadth (b') = 5m

Area = length × breadth

= 120 × 5

= 600 m²

We know that ,

Both the roads are intersecting so the area of PQRS is occurring two times.

Thus, we have to subtract its area once.

Each side of PQRS square is 5m,

Area of PQRS = (side)²

= (5)²

= 25 m²

Now,

The area of the road to be constructed is,

= (Area of BCGH + Area of EFIJ) - Area of PQRS

= 400 + 600 - 25

= 1000 - 25

= 975 m²

The cost of constructing the road for 1 m sq is Rs. 120

The cost for constructing the road for 975 m sq, will be

= 975 × 120

= Rs. 117000