Question 26

If p squares of each side 1 mm make a square of side 1cm, then p is equal to

(a) 10
(b) 100
(c) 1000
(d) 10000

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Solution

$∵$ Area of 1 square of side $1 m m = 1 \times 1 m m^{2} = 1 m m^{2}$ $[∵ a r e a o f s q u a r e = (s i d e)^{2}]$
Area of square of side $1 c m = 1 \times 1 c m^{2} = 1 c m^{2}$ $[∵ a r e a o f s q u a r e = (s i d e)^{2}]$
According to the question,
Area of p squares of side 1mm = Area of square side 1 cm
$\Rightarrow p \times 1 m m^{2} = 1 c m^{2} \Rightarrow p m m^{2} = 1 c m^{2}$
$\Rightarrow p m m^{2} = (10 m m)^{2}$ $[∵ 1 c m = 10 m m]$
$\Rightarrow p m m^{2} = (100 m m)^{2}$
So, p = 100

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