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What is the value of x?

Enter your answer, as a decimal, in the box.

 ?cm  

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(I just added the pic - Melody)

Guest Jan 16, 2018
edited by Guest  Jan 16, 2018
edited by Melody  Jan 16, 2018

Best Answer 

 #1
avatar+2248 
+1

\(\triangle MNP\sim\triangle MAB\) because a segment located in the interior of the triangle is parallel to a side. You could also prove similarity by Angle-Angle Similarity Theorem. 

 

Using the above similarity statement, one can create a proportion because each side is proportional. The one I will use is \(\frac{MA}{MB}=\frac{MN}{MP}\). This comes from the similarity statement. 

 

Although we do not know the length of \(\overline{MA}\) directly, we can find it by subtracting the length of \(\overline{AN}\) from the length of \(\overline{MN}\). When we plug in these numbers, we can then solve for the unknown side length.

 

\(\frac{MA}{MB}=\frac{MN}{MP}\) Plug in the known information and solve for the unknown.
\(\frac{46.2-14}{x}=\frac{46.2}{72.6}\) Let's simplify the numerator of the left hand side of the equation first.
\(\frac{32.2}{x}=\frac{46.2}{72.6}\) Before proceeding, it may be wise to multiply the fractions by 10/10 so that the numbers are whole numbers.
\(\frac{322}{10x}=\frac{462}{726}\) Some simplification can occur here. The numerator and denominator of the right hand side happen to have a greatest common factor of 66. That's something you don't see every day!
\(\frac{161}{5x}=\frac{7}{11}\) Now, let's do the cross multiplication with simplified numbers.
\(1771=35x\) Divide by 35 from both sides.
\(x=\frac{1771}{35}=\frac{253}{5}=50.6\)  
   
TheXSquaredFactor  Jan 17, 2018
 #1
avatar+2248 
+1
Best Answer

\(\triangle MNP\sim\triangle MAB\) because a segment located in the interior of the triangle is parallel to a side. You could also prove similarity by Angle-Angle Similarity Theorem. 

 

Using the above similarity statement, one can create a proportion because each side is proportional. The one I will use is \(\frac{MA}{MB}=\frac{MN}{MP}\). This comes from the similarity statement. 

 

Although we do not know the length of \(\overline{MA}\) directly, we can find it by subtracting the length of \(\overline{AN}\) from the length of \(\overline{MN}\). When we plug in these numbers, we can then solve for the unknown side length.

 

\(\frac{MA}{MB}=\frac{MN}{MP}\) Plug in the known information and solve for the unknown.
\(\frac{46.2-14}{x}=\frac{46.2}{72.6}\) Let's simplify the numerator of the left hand side of the equation first.
\(\frac{32.2}{x}=\frac{46.2}{72.6}\) Before proceeding, it may be wise to multiply the fractions by 10/10 so that the numbers are whole numbers.
\(\frac{322}{10x}=\frac{462}{726}\) Some simplification can occur here. The numerator and denominator of the right hand side happen to have a greatest common factor of 66. That's something you don't see every day!
\(\frac{161}{5x}=\frac{7}{11}\) Now, let's do the cross multiplication with simplified numbers.
\(1771=35x\) Divide by 35 from both sides.
\(x=\frac{1771}{35}=\frac{253}{5}=50.6\)  
   
TheXSquaredFactor  Jan 17, 2018

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