Question

The perimeters of two squares are 120 and 160 meters respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Answer 1

$Let \: a \: and \: s \: are \: sides \: of \: two$

$squares .$

$i)Perimeter \: of \: One \: square \: whose \\side \: is \: 'a' = 120 \:m$

$\implies 4a = 120$

$\implies a = \frac{120}{4}$

$\implies a = 30 \:m \: --(1)$

$ii) Perimeter \: of \: Second \: square \: whose \\side \: is \: 's' = 160 \:m$

$\implies 4s = 160$

$\implies s = \frac{160}{4}$

$\implies s = 40 \:m \: --(2)$

/* According to the problem given */

$\blue{ iii) Area \: of \: New \: square}\\\blue{ = sum \: of \: the \: area \: of \: two \:squares }$

$= a^{2} + s^{2} \\= 30^{2} + 40^{2} \\= 900 + 1600 \\= 2500 \: m^{2}$

$\pink{ Side \: of \: new \: square } = \sqrt{ 2500 \: m^{2} }$

$= 50\: m$

$\red{Perimeter \: of \: new \: square } \\= 4 \times 50 \:m \\= 200 \: m$

Therefore.,

$\red{Perimeter \: of \: new \: square } \\\green { = 200 \: m}$

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