Question

A rectangular plot of 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 pilot is used as a lawn. If the ara of the lawn is 1911m2,
what is the width of each of hte crossroads?
(a) 5 m
(b) 5.5 m
(c) 6 m
(d) 4 m
(e) 4.5 m

Answer 1

Let the width of the crossroad be X. Since there is two crossroads, one parallel to the length and the other parallel to the breadth, the actual length and breadth of the lawn is(55-x)m and (45-x)m.
$(55 - x)(45 - x) = 1911 \\ (x - 55)(x - 45) = 1911 \\ {x}^{2} - 100x + 2475 = 1911 \\ {x}^{2} - 100x + 564 = 0 \\ (x - 94)(x - 6) = 0 \\ ie. \: x = 94 \: or \: 6$
width of crossroad cannot be 94, therefore the answer is 6.