SOLUTION: I dont understand this, can someone walk me through and show their work? https://docs.google.com/document/d/11ubufkDLZVRNKRWGP-FQS1OdG1R5iG1z-dD6d_yCxVY/edit?usp=sharing That is

Algebra ->  Triangles -> SOLUTION: I dont understand this, can someone walk me through and show their work? https://docs.google.com/document/d/11ubufkDLZVRNKRWGP-FQS1OdG1R5iG1z-dD6d_yCxVY/edit?usp=sharing That is      Log On


   

Question 1034432: I dont understand this, can someone walk me through and show their work?
https://docs.google.com/document/d/11ubufkDLZVRNKRWGP-FQS1OdG1R5iG1z-dD6d_yCxVY/edit?usp=sharing
That is the link for the question, it's a picture question so i couldn't upload it on here, thank you in advance!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The problem says that triangles MNP and XYZ are similar.
The corresponding vertices are given in the same order,
so M correspond to X} ,
and the angles at those vertices are congruent (have the same measure).
The same is true for N and Y%7D%7D+%2C+and+for+%7B%7B%7BP and Z .
Sides MP and XZ are corresponding sides.
So are sides NP and YZ .
Besides angles having the same measure,
the fact that the triangles are similar means that
triangle MNP is a scaled up or scaled down version of triangle XYZ .
The scaling factor ismthe ratio of lengths of the corresponding sides:
MP%2FXZ=NP%2FYZ .
On the figure, the lengths of those sides are shown as:
MP=x%2B5
NP=4x-10
XZ=30
YZ=75 .
So, %28x%2B5%29%2F30=%284x-10%29%2F75
From that equation, we solve for x .
First, we eliminate denominators by multiplying times a common multiple of the denominators,
2%2A75=150=5%2A30 .
%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 .
The rest is easy:
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