Math, asked by harshvardhannarware2, 1 month ago

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

Answers

Answered by hraj65794
0

Answer:

Step-by-step explanation:

Let the width of the gravel path be x m.

Each Sides of the square flower bed = (44 - 2x) m.

Area of the square field= side × side

Area of the square field= 44× 44 = 1936 m²

Area of flower bed = (44-2x)² = 1936 -176x+4x²

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

= 1936 - (1936 - 176x + 4x²)

= 1936 - 1936 + 176x - 4x²

= 176 x - 4x²

Cost of laying the flower bed =( Area of the flower bed) × ( rate per square metre)

= (44-2x)² × 2.75

=( 275/100)(44-2x)²

= 11/4 × (44-2x) (44-2x)

= 11/4 ×2 (22 -x) 2 (22 -x)

= 11/4 ×4 (22 -x)²

= 11(22-x)²

Cost of graveling the path =( Area of the path) × ( rate per square metre)

= (176x - 4x²) × 150/100

= 4 (44x -x²) × 3/2

= 4 × 3/2 × (44x -x²)

= 6× (44x -x²)

Given = the total cost of laying the flower bed and gravelling the path is ₹ 4904.

11(22-x)² + 6× (44x -x²) = 4904

= 11(484 - 44 x +x²) + (264x - 6x²)= 4904

= 11(484 - 44 x +x²) +6 (44x - x²)= 4904

= 5x² -220x + 5234 = 4908

= 5x² -220x +420 = 0

= x² - 44x +84= 0

= x² -42x -2x +84=0

= x( x-42) -2(x-42)=0

= (x-2) (x-42)= 0

= x= 2 or x= 42

But x≠42, as the side of the square is 44 m. Therefore x= 2

Hence, the width of the gravel path is 2 m.

HOPE THIS WILL HELP YOU..

Answered by raghudibbur3
0

Answer:

Step-by-step explanation:

Similar questions