Answer:
B
Step-by-step explanation:
The first thing the man needs to do
Is to arrange the books by Abraham Lincoln amongst each other first. Now the number of ways the man can arrange these books amongst each other is a total of 4! Ways. Now there are 6 books remaining and there are also six slots remaining. The number of ways to arrange these six books within theirselves would be 6!
Now the total
Number of arrangements is 6! * 4!
Answer:
1100 mm = 1.1 m, and 900 mm = 0.9 m.
So the area is 1.1 x 0.9 = 0.99 m^2
bearing in mind that there are 90 feet between each base in a baseball diamond, so the total perimeter of it will be 90*4 = 360, one third of that is 360/3 = 120.
So Jones went 120 feet first and then another and so on, check the picture below.
using those values, can get the length of those sides, using the pythagorean theorem.
![\bf AH=\sqrt{HF^2+FA^2}\implies AH=\sqrt{9000} \\\\\\ AB=\sqrt{AS^2+SB^2}\implies AB=\sqrt{7200} \\\\\\ HB = AH = \sqrt{9000} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{perimeter}{\sqrt{9000}+\sqrt{7200}+\sqrt{7200}}\qquad \approx \qquad \stackrel{perimeter}{264.57}](https://tex.z-dn.net/?f=%5Cbf%20AH%3D%5Csqrt%7BHF%5E2%2BFA%5E2%7D%5Cimplies%20AH%3D%5Csqrt%7B9000%7D%20%5C%5C%5C%5C%5C%5C%20AB%3D%5Csqrt%7BAS%5E2%2BSB%5E2%7D%5Cimplies%20AB%3D%5Csqrt%7B7200%7D%20%5C%5C%5C%5C%5C%5C%20HB%20%3D%20AH%20%3D%20%5Csqrt%7B9000%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7Bperimeter%7D%7B%5Csqrt%7B9000%7D%2B%5Csqrt%7B7200%7D%2B%5Csqrt%7B7200%7D%7D%5Cqquad%20%5Capprox%20%5Cqquad%20%5Cstackrel%7Bperimeter%7D%7B264.57%7D)
now, we can plug those values in the Heron's Area Formula to get its area.
![\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{9000}\\ b=\sqrt{7200}\\ c=\sqrt{7200}\\ s\approx 132.29 \end{cases} \\\\\\ A=\sqrt{132.29(132.29-\sqrt{9000})(132.29-\sqrt{7200})(132.29-\sqrt{7200})} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 3337.289~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BHeron%27s%20area%20formula%7D%20%5C%5C%5C%5C%20A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5Cqquad%20%5Cbegin%7Bcases%7D%20s%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D%5Csqrt%7B9000%7D%5C%5C%20b%3D%5Csqrt%7B7200%7D%5C%5C%20c%3D%5Csqrt%7B7200%7D%5C%5C%20s%5Capprox%20132.29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B132.29%28132.29-%5Csqrt%7B9000%7D%29%28132.29-%5Csqrt%7B7200%7D%29%28132.29-%5Csqrt%7B7200%7D%29%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20A%5Capprox%203337.289~%5Chfill)
The short answer is trial and error. The side lengths "3" and "4" can both be substituted for a² and b² but not c² because their value squared is not high enough since 5² is 25. "c²" as to match the longest side because the smaller numbers will cause the equation to not be true. See Below.
a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
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a² + b² = c²
4² + 3² = 5²
16 + 9 = 25
25 = 25
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a² + b² = c²
5² + 4² = 3²
25 + 16 = 9
41 ≠ 9
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a² + b² = c²
3² + 5² = 4²
9 + 25 = 16
34 ≠ 16
Hope this helped!
