Question

Ben had two copies of the same poster in different sizes. Both posters are in the shape of a square. The side length of the two posters is in the ratio of 3:7. If the perimeter of the smaller poster is 27 cm, what is the perimeter of the bigger poster?

Answer 1

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the question states that a person named Ben has two copies of the same poster having different sizes , provided they both are squares !

further , we've been given that the side length of the posters are in the ratio of 3:7 and the perimeter of the smaller posted is 27 cm .

We've been asked to find the perimeter of the bigger poster !

so let's start ~

`let\: the \: length \: of \: the \: smaller \: poster \: be \: 3x \\ \\ let \: the \: length \: of \: the \: bigger \: poster \: be \: 7x \\ \\ now \: , \: \\ \\ perimeter \: of \: square = 4 * side \\ \\ \implies \: perimeter \: of \: shorter \: square = 4 * 3x \\ \\ \implies \: 27 = 3x \\ \\ x = \cancel(27)/(3) \\ \\ \implies\red{\boxed{ \: x = 9 \: cm}}`

now ,

`side \: length \: of \: bigger \: square = 7x \\ \\ \implies \: 7 * 9 = 63 \: cm \\ \\ \therefore \: perimeter \: of \: bigger \: square = 4 * 63 \\ \\ \bold\pink{\implies \: 252 \: cm}`

hope helpful :D