Question

The sides of a rectangular park are in the ratio 3:2.If its area is 1176 sq m ,find the cost of fencing it at rupees 3.50 per metre.

Answer 1

Answer:

The cost of fencing the park is Rs 490.

Step-by-step explanation:

It is given that the ratio of sides of rectangular park is 3 : 2.

We know, length is the longest side, it can't be smaller than any other side.

So,

Let the length of the park be 3 a

           breadth of the park be 2 a

We know,

Area of rectangle = length x breadth

Hence,

Area of the park = 3 a x 2 a

Area of the park = 6a^2     ...( i )

According to the question : -

Area of the park is 1176 m^2

Area of the park = 1176 m^2   ...( ii )

Now, comparing ( i ) and ( ii ),

= >  6a^2 = 1176 m^2

= >  a^2 = 1176 m^2 / 6

= >  a^2 = 196 m^2

= >  a^2 = ( 14 m )^2 or ( - 14 m )^2

As 'a' is assumed as the length of the rectangle, it can't be negative.

So,

a = 14 m

Therefore,

Length of the park = 3 a = 3( 14 m ) = 42 m

Breadth of the park = 2 a = 2( 14 m ) = 28 m

Now,

Perimeter of the rectangle = 2( length + breadth )

           ⇒ 2( 42 m + 28 m )

           ⇒ 2( 70 m )

           ⇒ 140 m

Therefore,

Cost of fencing = rate of fencing x area to be fenced

Cost of fencing = Rs 3.5 / m x 140 m

Cost of fencing = Rs 3.5 x 140

Cost of fencing = Rs 490

Therefore, the cost of fencing the park is Rs 490.

Answer 2

Let sides be 3x and 2x
Area=l×b

l=3x(Since length is always longer)
b=2x
Area=1176m²

1176m²=(3x)×(2x)
1176=6x²
1176/6=x²
196=x²
√14×14=x
14=x

Length=3x=>3×14=>42cm
Breath=2x=>2×14=>28cm

Perimeter=2(l+b)
Perimeter=2(42+28)
Perimeter=2(70)
Perimeter=140m

So, cost of fencing
→140×3.50
→rs.490