in the centre of a square garden is a square lawn. outside this is a gavel walk 4dm wide and hen a flower border 6dm wide. If the flower border and lawn together contains 721 Sq. dm, find th side of the lawn

Dear student,

Please find below the solution to the asked query:

Consider a square lawn ABCD with side 'x dm' outside this is a gavel walk 4 dm wide and then a flower border 6 dm wide.The figure is shown below:

To differentiate the three, the lawn is red colored, the gavel walk is in blue colorand the flower border is green in color.The area of the lawn is    x×x= x2 The area of the flower border is,    area of square IJKL-Area of square EFGH   =x+2×4+2×62-x+2×42   =x+8+122-x+82   =x+202-x+82   =x2+40x+400-x2+16x+64   =x2+40x+400-x2-16x-64   =24x+336Accoding to given condition, we get             x2 +24x+336=721   x2 +24x+336-721=0             x2 +24x-385=0 Factorize the LHS to get,      x2 +35x-11x-385=0      xx+35-11x-35=0                x-11x-35=0                                      x=11, -35Neglect the -ve value to get  x=11 dmThus the side of the lawn is 11 dm

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