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Observe the following pattern in which each small square represents a unit square (square of side $1$ unit).
Fig (i)
Fig (ii)
Fig (iii)
and so on
If the sum of number of unit squares in the $n^{th}$ figure and $(n + 2)^{th}$ figure is $290$, find the value of $n$.
Fig (i)
Fig (ii)
Fig (iii)
and so on
If the sum of number of unit squares in the $n^{th}$ figure and $(n + 2)^{th}$ figure is $290$, find the value of $n$.
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Solution: (b) Number of unit squares in the $n^{th}$ figure $= n^2$ (1/2 Mark)
Number of unit squares in the $(n + 2)^{th}$ figure $= (n + 2)^2$ (1/2 Mark)
As per the given condition,
$n^2 + (n + 2)^2 = 290$ (1 Mark)
$n^2 + 2n - 143 = 0$ (1 Mark)
$(n + 13)(n-11) = 0$ (1 Mark)
$n = 11, -13$ (rejected) (1 Mark)
Number of unit squares in the $(n + 2)^{th}$ figure $= (n + 2)^2$ (1/2 Mark)
As per the given condition,
$n^2 + (n + 2)^2 = 290$ (1 Mark)
$n^2 + 2n - 143 = 0$ (1 Mark)
$(n + 13)(n-11) = 0$ (1 Mark)
$n = 11, -13$ (rejected) (1 Mark)