What is the ratio of the corresponding side lengths

Mathematics
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The areas of corresponding faces of 2 similar pentagonal prisms are 49 inches squared and 25 inches squared. 

May 17th, 2015

You are given the areas of the pentagonal prism faces. They are 49 in^2 and 25 in^2. The area of a pentagon is (1/4)(the square root of (5(5+2 root (5))))(a^2) where a equals a side length. You have to solve this equation for both pentagons. The part before a^2 equals 1.7204774005889669227590119773886

The first is 49 = 1.7204774005889669227590119773886a^2 solving for a you get a = 5.336709388547417121488818775112

The second is 25 = 1.7204774005889669227590119773886a^2 so a = 3.8119352775338693724920134107943

Then you divide them by each other to get the ratio

5.336709388547417121488818775112 / 3.8119352775338693724920134107943 = 1.4

The ratio between the 49 and 25 is 1.4 to 1 or 1.4:1

If you need the ratio in a whole number you can multiply it by however many times it will take to make the decimal go away. In this case it is by 5. 1.4 * 5 = 7. and then 1 * 5 = 5

A whole number ratio between the two is 7:5

I hope this helps! Please let me know if you have any questions :)

May 17th, 2015

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