in the centre of a square garden is a square lawn outside this is a gavel walk 4dm wide - Maths - Quadratic Equations

Question

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

Vijay Kumar Gupta · Accepted Answer

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:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5638ebe663774%20png"
style="width: 200px; height: 193px;">

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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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