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?

How much will it cost to make a gravel track 2 m wide around the insid

1.	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?
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 × sideArea of the square field= 44× 44 = 1936 m²Area of flower bed = (44-2x)² = 1936 -176x+4x²Area of the gravel path = area of the square field - area of the flower bed= 1936 - (1936 - 176x + 4x²) = 1936 - 1936 + 176x - 4x² = 176 x - 4x²Cost 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)²Cost 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= 42But 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..