Question

how much will it cost to make a gravel track 2 m wide around the inside of a square field whose area is 14400m² at the rate of rupees 3 per m² ?​

Answer 1

Answer:

2m

Step-by-step explanation:

Let us assume the gravel path’s width to be x m. Since the flower bed is in the centre of the square field with a gravel path surrounding it. So each side of the flower bed is= side of a square field- 2(width of gravel).

⇒ Each Side of the flower bed=44−2x m

Then the area of flower bed=(44−2x)²

m {as the area of square=side2}

And the area of the square field

=44×44=1936sq.m.

Then the area of gravel path=area of square field-area of flower bed

⇒ Area of gravel path=1936−(44−2x)2=1936−1936+176x - 4x2

On simplifying, we get

⇒ Area of gravel path=176−4x2 sq.m.

Then the area of gravel path=area of square field-area of flower bed

Now, the cost of laying flower bed=area of flower bed × rate per sq. m. and we can write rate as2.75=275100 .Then on putting the values, we get-

⇒ The cost of layingflowerbed

=(44−2x)2×275/100=11/4(44−2x)²=11

And the cost of laying gravel path=area of gravel path × rate per sq. m. We can write rate as1.50=150100 .Then on putting values, we get-

⇒ Cost of laying gravel path

=(176−4x2)150100=6(44−x2)=264−

According to the question we know that the total cost of laying flower bed and gravel path

=4904 Rs.

So,

⇒11(22−x)2+264−6x2=4904

On solving the eq. we get,

⇒11(484+x2−44x)+264−6x2=4904

⇒5324+11x2−484x +264−6x2=4904

⇒5x2−220x + 5324 = 4904

⇒5x2−220x + 420 = 0

On dividing the eq. by 5, we get-

⇒x2−44x + 84 = 0

By factoring, we get-

• ⇒x2−42x - 2x + 84 = 0
• ⇒x(x - 42)−2(x - 42)=0
• ⇒(x - 42)(x - 2)=0
• ⇒x = 42 or x=2

But since the side of the square field =44 m so the width of gravel path cannot be longer than that.

So the width of gravel path =2m.

$2m$

Hope its help u

Answer 2

Answer:

2

Step-by-step explanation:

I don't know bye sorry ok