document.write( "Question 1034432: I dont understand this, can someone walk me through and show their work?
\n" ); document.write( "https://docs.google.com/document/d/11ubufkDLZVRNKRWGP-FQS1OdG1R5iG1z-dD6d_yCxVY/edit?usp=sharing
\n" ); document.write( "That is the link for the question, it's a picture question so i couldn't upload it on here, thank you in advance! \n" ); document.write( "

Algebra.Com's Answer #649073 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The problem says that triangles $\"MNP\"$ and $\"XYZ\"$ are similar.
\n" ); document.write( "The corresponding vertices are given in the same order,
\n" ); document.write( "so $\"M\"$ correspond to $\"X\"$ } ,
\n" ); document.write( "and the angles at those vertices are congruent (have the same measure).
\n" ); document.write( "The same is true for $\"N\"$ and $\"Y%7D%7D+%2C+and+for+%7B%7B%7BP\"$ and $\"Z\"$ .
\n" ); document.write( "Sides $\"MP\"$ and $\"XZ\"$ are corresponding sides.
\n" ); document.write( "So are sides $\"NP\"$ and $\"YZ\"$ .
\n" ); document.write( "Besides angles having the same measure,
\n" ); document.write( "the fact that the triangles are similar means that
\n" ); document.write( "triangle $\"MNP\"$ is a scaled up or scaled down version of triangle $\"XYZ\"$ .
\n" ); document.write( "The scaling factor ismthe ratio of lengths of the corresponding sides:
\n" ); document.write( " $\"MP%2FXZ=NP%2FYZ\"$ .
\n" ); document.write( "On the figure, the lengths of those sides are shown as:
\n" ); document.write( " $\"MP=x%2B5\"$
\n" ); document.write( " $\"NP=4x-10\"$
\n" ); document.write( " $\"XZ=30\"$
\n" ); document.write( " $\"YZ=75\"$ .
\n" ); document.write( "So, $\"%28x%2B5%29%2F30=%284x-10%29%2F75\"$
\n" ); document.write( "From that equation, we solve for $\"x\"$ .
\n" ); document.write( "First, we eliminate denominators by multiplying times a common multiple of the denominators,
\n" ); document.write( " $\"2%2A75=150=5%2A30\"$ .
\n" ); document.write( " $\"%28x%2B5%29%2F30=%284x-10%29%2F75\"$ <--> $\"150%2A%28x%2B5%29%2F30=150%2A%284x-10%29%2F75\"$ <--> $\"5%2A%28x%2B5%29=2%2A%284x-10%29\"$ <--> $\"5x%2B25=8x-20%29\"$ .
\n" ); document.write( "The rest is easy:
\n" ); document.write( " $\"5x%2B25=8x-20%29\"$ <--> $\"5x%2B25-5x%2B20=8x-20-5x%2B20%29\"$ <--> $\"25%2B20=8x-5x%29\"$ <--> $\"45=3x%29\"$ <--> $\"45%2F3=x\"$ ,--> $\"highlight%28x=15%29\"$ \n" ); document.write( "

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