Kim has 437.5 miles to drive until she arrives at home she drives 70 miles per hour and does not stop

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ogpuhl

26.09.2020

Mathematics

$a. \ \ \ P_l=954 \ ft\\\\b.\ A_s=944 \ ft^2$

Step-by-step explanation:

a. Given that the area's are in the ratios 16:81.

-Area is two-dimensional while perimeter is one-dimensional

=>The perimeter's of the two polygons will vary in a ratio equal to the square root of their area's ratio:

$P_s:P_b=\sqrt{A_s}:\sqrt{A_b}\\\\=\sqrt{16}:\sqrt{81}\\\\=4:9$

We use the perimeter ratio to find the perimeter of the larger polygon:

$\frac{P_s}{P_l}=\frac{4}{9}=\frac{424}{P_l}\\\\P_l=(424\times 9)/4\\\\=954\ ft$

Hence, the perimeter of the larger polygon is 954 ft

b -Given the area of the larger polygon is 4779 ft2, the smaller polygon can be determined using the area ratio 16:81

$\frac{A_s}{A_l}=\frac{A_s}{4779}=\frac{16}{81}\\\\A_s=\frac{4779\times 16}{81}\\\\=944$

Hence, area of the smaller polygon is $944 \ ft^2$

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