anonymous
  • anonymous
Use the Triangle Proportionality Theorem to solve for x. A. x = 2 B. x = 2.5 C. x = 3 D. x = 3.5
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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Kuoministers
  • Kuoministers
4/6=6/(6+x)
Kuoministers
  • Kuoministers
just work out what x equals and thart is your answe

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mathstudent55
  • mathstudent55
The two triangles are similar, so their corresponding sides are proportional. That means 4 is to 2 as 4 + 2 is to 6 + x or as an equation, 4/2 = (4+ 2)/(6 + x) Cross multiply and solve for x.
anonymous
  • anonymous
how do i croos multiply? could you five me the solution?
Kuoministers
  • Kuoministers
@mathstudent55 wouldnt it be 4/6 not 4/2? Because its 4 over the whole length of the side which is 6? 4+2
mathstudent55
  • mathstudent55
You are absolutely correct. Let me do it again. The two triangles are similar, so their corresponding sides are proportional. That means 4 is to 6 as 4 + 2 is to 6 + x or as an equation, 4/6 = (4+ 2)/(6 + x) Cross multiply and solve for x.
mathstudent55
  • mathstudent55
Interstingly enough, this simpler proportion also works: 4/2 = 6/x because the segments measuring 2 and x are also in the same ratio as the sides measuring 4 and 6 and the sides measuring 4 + 2 and 6 + x
anonymous
  • anonymous
so should I do 4*6=2*x
Kuoministers
  • Kuoministers
\[\huge\frac{ 4 }{ 6 } = \frac{ 6 }{ 6 + x }\]
anonymous
  • anonymous
I got x=3
Kuoministers
  • Kuoministers
Now we cross multiply and divide everything by 4 \[\huge4(6 + x) = 36\] \[\huge6 + x = 9\] now find x
mathstudent55
  • mathstudent55
|dw:1359442199584:dw|
Kuoministers
  • Kuoministers
both ways give you x=3 so its your choice to see which way you liked better.
Kuoministers
  • Kuoministers
\[\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{green}{\color{blue}T{\color{purple}H{\color{pink}A{\color{red}NK{\color{orange}S}}}}}}}}}} \]
anonymous
  • anonymous
HAHA cool!

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