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Sedbober [7]
3 years ago
6

How many triangles can be constructed with three sides measuring 11 meters,16 meters,and 26 meters?

Mathematics
1 answer:
topjm [15]3 years ago
5 0

You can only construct one triangle with three sides measuring 11 meters,16 meters, and 26 meters.

 

To add, a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted.

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How do you find the equation of a triangles altitude using point slope formula?
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<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047)   (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle: 

 

Let point 
A=(xA,yA)
B=(xB,yB)
C=(xC,yC) 



------------------------------- 
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Start with the general formula 

 


Plug in the given points 

 


Simplify and combine like terms 

 


So the equation of the line through AB is  


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Let's find the equation of the segment BC 


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Plug in the given points 

 


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So the equation of the line through BC is  




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Let's find the equation of the segment CA 


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Plug in the given points 

 


Simplify and combine like terms 

 


So the equation of the line through CA is  




So we have these equations of the lines that make up the triangle 


 



So to find the equation of the line that is perpendicular to  that goes through the point C(2,-5), simply negate and invert the slope  to get 

Now plug the slope and the point (2,-5) into  


 

 Solve for y and simplify 

So the altitude for vertex C is  



Now to find the equation of the line that is perpendicular to  that goes through the point A(4,5), simply negate and invert the slope to get  

Now plug the slope and the point (2,-5) into  


 

 Solve for y and simplify 

So the altitude for vertex A is  




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 Solve for y and simplify 

So the altitude for vertex B is  



------------------------------------------------------------ 
Now let's solve the system 


 

 Plug in  into the first equation 

 Add 2x to both sides and subtract 2 from both sides 

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Now plug this into  

 

 



So the orthocenter is (-2/3,1/3) 

So if we plug in  into the third equation , we get 


 


 


 

 

So the orthocenter lies on the third altitude 





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3 0
3 years ago
three friends jogged last month. Richard jogged 9 miles last month. Jena jogged 2 times as many miles as Richard. Brian jogged 4
ANTONII [103]

Answer:

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Step-by-step explanation:

well if you add what Richard got and double it (9+9=18 or 9x2=18) you get how much Jena ran. then if u add (9+9+9+9=36 or 9x4=36) you get Brians miles he ran


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Answer:

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7 0
3 years ago
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