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Anastasy [175]
3 years ago
7

Pleaseeee help asap !! i’ll mark brainliest

Mathematics
1 answer:
Blizzard [7]3 years ago
6 0

Answer:

Step-by-step explanation:

C, (1,7)

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Read 2 more answers
The triangles are similar. What is the value of x? Enter your answer in the box. x = two right triangles. the larger triangle ha
grandymaker [24]
<h2><u>Answers:</u></h2>

These problems can be solved by the Thales’s Theorem, which states:



<em>Two triangles are similar when they have equal angles and proportional sides  </em>

In addition, i<u>f two triangles are similar, their angles are similar as well</u>. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle, as follows:  


\frac{B}{A}=\frac{b}{a}


Knowing this, lets’s begin with the answers:



1. For this first problem, see the <u>first figure attached</u>. There are shown the two triangles, and we are told both are similar, this means (according the prior explanation above) that we can use the Thale’s Theorem to find x.  


Therefore, we can establish a relation between two sides of the big triangle which is equal to the relation between two sides of the small triangle; in this case let’s use B and C for the first triangle and b and c for the second:




\frac{C}{B}=\frac{c}{b}



\frac{6x+28}{96}=\frac{25}{24}    


Now we find x:



6x+28=\frac{(25)(96)}{24}    


6x+28=100    


6x=100-28    


x=\frac{72}{6}    


x=12    

Finally, the value of x is 12 units.




2. For this problem, see <u>the second figure attached</u>. In order to find the values of the segments BE and EC, we will use two sides of each triangle (ABE and DCE) according to the Thale’s Theorem:



<u>For the segment BE:</u>



\frac{BE}{10}=\frac{x+3}{4}



BE=\frac{(x+3)(10)}{4}



Simplifying:



BE=\frac{5}{2}(x+3)  >>>>>This is the length of the segment BE


<u>For the segment EC:</u>



\frac{EC}{4}=\frac{2x+10}{10}



EC=\frac{(2x+10)(4)}{10}



Simplifying:



EC=\frac{4}{5}(x+5)>>>>>This is the length of the segment EC


3. For this problem, see the <u>third figure attached:</u>


\frac{12 inches}{8 inches}=\frac{x}{7 inches}



Solving for x:

x=\frac{(12 inches)(7 inches)}{8 inches}



Finally:

x=10.5 inches>>>>>This is the height of the smaller sail



4. For this problem, see the <u>fourth figure attached.</u>



\frac{80 inches}{45 inches}=\frac{x}{40 inches}



Solving for x:

x=\frac{(80 inches)(40 inches)}{45 inches}



x=71.11 inches  >>>>>This is the height from the floor to the son's hand



6 0
3 years ago
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