Question

A rectangle plot 55 m long and 45 m broad, has two concrete crossroads (of equal width) running in the middle of it. One parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the area of the lawn is 1911 m2, what is the width of each of the crossroads?
(a) 5m
(b) 5.5m
(c) 6m
(d) 4m
(e) 4.5m

Answer 1

Let the width of each cross road be ' x '




Given ,






length of rectangular plot = 55 m






breadth of rectangular plot = 45 m





area of cross road
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= 55 × x + 45 × x - ( area of square that is there in centre and sharing area with two cross roads )






= 55 × x + 45 × x - x × x






= 55 x + 45 x - x^2






=( 100 x - x^2 ) m^2






Given ,area of lawn = 911 m^2







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area of lawn = area of rectangular plot - area of cross road )
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911 m ^2 = length × breadth - ( 100 x - x^2






911 = 55 × 45 - 100x + x^2






x^2 - 100 x + 2475 - 911 = 0





x^2 - 100 x + 564 = 0









x^2 - 94 x - 6 x + 564 = 0






x ( x - 94 ) - 6 ( x - 94 ) = 0












( x - 6 ) ( x - 94 ) = 0







x = 6 m , x = 94 m ( neglect it )








x = 94 m ,its too big , its not possible , because width of cross road will be shorter than the width of plot (45m)
so we can neglect this value.





therefore ,








the width of each crossroad x = 6 m




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Your Answer option (c ) 6 m
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