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Answer 1 · 2018-02-16T20:10:37

$12.57 cm$ $12.57" cm"$

Explanation:

$given two similar figures then$ $"given two similar figures then "$

$∙ linear ratio = a : b$ $• "linear ratio "=a:b$

$∙ area ratio = a^{2} : b^{2}$ $• " area ratio "=a^2:b^2$

$∙ volume ratio = a^{3} : b^{3}$ $• " volume ratio "=a^3:b^3$

$here area ratio = 49 : 16$ $"here area ratio "=49:16$

$\Rightarrow linear ratio = \sqrt{49} : \sqrt{16} = 7 : 4$ $rArr"linear ratio "=sqrt49:sqrt16=7:4$

$\Rightarrow \frac{larger part of ratio}{smaller part of ratio} = \frac{larger perimeter}{smaller perimeter}$ $rArr"larger part of ratio"/"smaller part of ratio"="larger perimeter"/"smaller perimeter"$

$we want the smaller perimeter (p)$ $"we want the smaller perimeter (p)"$

$\Rightarrow \frac{7}{4} = \frac{22}{p} \leftarrow cross multiply$ $rArr7/4=22/plarrcolor(blue)"cross multiply"$

$\Rightarrow 7 p = 4 \times 22$ $rArr7p=4xx22$

$\Rightarrow p = \frac{4 \times 22}{7} \approx 12.57 cm to 2 dec. places$ $rArrp=(4xx22)/7~~12.57" cm to 2 dec. places"$

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