Question

If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :​

Answer 1

Sorry for a little hazy pic. The answer is 15:16. Click to view full photo.

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Answer 2

$\small \bigstar \small \sf \purple{ \: Solution:- }$

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$\small \purple \bigstar \small \sf{ \: Let \: side \: of \: squares \: are} \purple{ \: a \: and \: b}{ \: respectively }$

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$\small\bigstar\small \sf \purple{ \: We \: know \: that \: area \: of \: square \: :- \: } \\ \sf{side × side}$

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$\small \purple \bigstar\small \sf{ \: Ratio \: of \: area \: of \: two \: squares = 225:256 }$

$\purple\leadsto\sf{ \frac{ {x}^{2} }{ {y}^{2} } = \frac{225}{256} }$

$\purple\leadsto\sf{ \frac{ x }{ y } = \frac{ \sqrt{225} }{ \sqrt{256} } }$

$\purple\leadsto \sf{ \frac{ x }{ y } = \frac{ 15 }{ 16} }$

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$\small \sf { \: \: \: \: \: \: \: \: \: \:\small \bigstar \: \purple{ Comparing \: both \: sides:- } \: } \\ \small\sf{ \: \: \: \: \: \: x = 15 \: and \: y \: = 16}$

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$\small \bigstar \small \sf \purple{ \: Now, Find \: ratio \: of \: their \: perimeters }$

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$\small \bigstar \small \sf \purple{ \: We \: know \: that \: perimeter \: of \: square \: :- \: } \\ \sf{4 × side}$

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$\small \purple \bigstar \small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares = 4x:4y }$

$\small \purple \bigstar \small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = \frac{4x}{4y} }$

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$\small \bigstar\small \sf \purple{ \: Substitute \: the \: value \: of \: x \: and \: y }$

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$\small \purple \bigstar\small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = \frac{4 \times 15}{4 \times 16} }$

$\small \purple \bigstar \small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = \frac{60}{64} }$

$\small \purple \bigstar \small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = \cancel \frac{60}{64} }$

$\small \purple \bigstar\small \sf{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = \frac{15}{16} }$

$\small\bigstar\small \sf \purple{ \: Ratio \: of \: perimeter \: of \: two \: squares}{ \: = 15:16 }$