Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - 10-4 Perimeters and Areas of Similar Figures - Practice and Problem-Solving Exercises - Page 639: 21

Answer

$\dfrac{7}{3}$ and $7: 3$

Work Step by Step

We can see that the ratio of the perimeters of two smaller figures is $\dfrac{a}{b}$, and the ratio of their areas is the square of the ratio of their perimeters: $\dfrac{a^2}{b^2}$. Set up a proportion: $\dfrac{a^2}{b^2}=\dfrac{49}{9} \\ \dfrac{a}{b}=\sqrt {\dfrac{49}{9}}$ This implies that the square factor is $ \dfrac{a}{b}=\dfrac{7}{3}$ So, the ratio of the perimeters is equal to the scale factor, which is $7: 3$
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