Darnell is building a triangular community garden plot.
Which set of lengths can be used to create the plot perimeter?
Recall the triangle inequality theorem which states that the sum of any two sides must be greater than the third side.
![\begin{gathered} a+b>c \\ b+c>a_{} \\ a+c>b \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%20b%2Bc%3Ea_%7B%7D%20%5C%5C%20a%2Bc%3Eb%20%5Cend%7Bgathered%7D)
Let us analyze each of the given options.
Option A:
a = 20 feet
b = 12 feet
c = 34 feet
![\begin{gathered} a+b>c \\ 20+12>34 \\ 32>34\quad (\text{not satified)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%2020%2B12%3E34%20%5C%5C%2032%3E34%5Cquad%20%28%5Ctext%7Bnot%20satified%29%7D%20%5Cend%7Bgathered%7D)
Option B:
a = 8 feet
b = 10 feet
c = 19 feet
![\begin{gathered} a+b>c \\ 8+10>19 \\ 18>19\quad (\text{not satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%208%2B10%3E19%20%5C%5C%2018%3E19%5Cquad%20%28%5Ctext%7Bnot%20satisfied%29%7D%20%5Cend%7Bgathered%7D)
Option C:
a = 5 feet
b = 8 feet
c = 14 feet
![\begin{gathered} a+b>c \\ 5+8>14 \\ 13>14\quad (\text{not satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%205%2B8%3E14%20%5C%5C%2013%3E14%5Cquad%20%28%5Ctext%7Bnot%20satisfied%29%7D%20%5Cend%7Bgathered%7D)
Option D:
a = 12, feet
b = 14 feet
c = 20 feet
![\begin{gathered} a+b>c \\ 12+14>20 \\ 26>20\quad (\text{satisfied)} \\ b+c>a \\ 14+20>12 \\ 24>12\quad (\text{satisfied)} \\ a+c>b \\ 12+20>14 \\ 22>14\quad (\text{satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%2012%2B14%3E20%20%5C%5C%2026%3E20%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5C%5C%20b%2Bc%3Ea%20%5C%5C%2014%2B20%3E12%20%5C%5C%2024%3E12%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5C%5C%20a%2Bc%3Eb%20%5C%5C%2012%2B20%3E14%20%5C%5C%2022%3E14%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5Cend%7Bgathered%7D)
As you can see, only option D satisfies the triangle inequality theorem
Therefore, option D is the correct answer.
Let the number be x .
Reciprocal of x :-
![= \frac{1}{x}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7Bx%7D%20)
An equation to find x :-
![2 \times \frac{1}{x} = 16 \times \frac{1}{20}](https://tex.z-dn.net/?f=2%20%5Ctimes%20%20%5Cfrac%7B1%7D%7Bx%7D%20%20%3D%2016%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B20%7D%20)
![\frac{2}{x} = \frac{16}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7Bx%7D%20%20%3D%20%20%5Cfrac%7B16%7D%7B20%7D%20)
![16 \times x = 20 \times 2](https://tex.z-dn.net/?f=16%20%5Ctimes%20x%20%3D%2020%20%5Ctimes%202)
![16x = 40](https://tex.z-dn.net/?f=16x%20%3D%2040)
![x = \frac{16}{40}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B16%7D%7B40%7D%20)
![x = \frac{4}{10}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4%7D%7B10%7D%20)
![x= \frac{4 \div 2}{10 \div 2}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B4%20%5Cdiv%202%7D%7B10%20%5Cdiv%202%7D%20)
![x = \frac{2}{5}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B2%7D%7B5%7D%20)
Reciprocal of x :-
![= \frac{5}{2}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20)
Which means the number :-
![= \frac{5}{2}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20)
We can check it by :-
![2 \times \frac{2}{5} = \frac{16}{20}](https://tex.z-dn.net/?f=2%20%5Ctimes%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B16%7D%7B20%7D%20)
![\frac{4}{5} = \frac{16}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B16%7D%7B20%7D%20)
![\frac{4}{5} = \frac{16 \div 4}{20 \div 4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B16%20%5Cdiv%204%7D%7B20%20%5Cdiv%204%7D%20)
![\frac{4}{5} = \frac{4}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%20)
LHS = RHS
Which means we have found the correct number .
Therefore , the value of the number , whose reciprocal multiplied by 2 gives 16 times the reciprocal of 20 is :-
<h2>
![= \frac{5}{2}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20)
</h2>
9.75 ft
Since the triangles formed by the heights and shadows, the ratios of corresponding sides are equal.
the corresponding sides are the heights and the lengths of the shadows
let h be the height of the tree, then
=
( cross- multiply )
12h = 4.5 × 26 = 117 ( divide both sides by 12 )
h = 9.75
hence the height of the tree is 9.75 ft
Answer:
1: 25
Step-by-step explanation:
100 : 25L
25L equal 2500 mL
100:2500 ( divide by 100)
1:25