## katlin95 2 years ago Use the Triangle Proportionality Theorem to solve for x. A. x = 2 B. x = 2.5 C. x = 3 D. x = 3.5

1. katlin95

2. Kuoministers

4/6=6/(6+x)

3. Kuoministers

just work out what x equals and thart is your answe

4. 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.

5. katlin95

how do i croos multiply? could you five me the solution?

6. 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

7. 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.

8. 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

9. katlin95

so should I do 4*6=2*x

10. Kuoministers

$\huge\frac{ 4 }{ 6 } = \frac{ 6 }{ 6 + x }$

11. katlin95

I got x=3

12. Kuoministers

Now we cross multiply and divide everything by 4 $\huge4(6 + x) = 36$ $\huge6 + x = 9$ now find x

13. mathstudent55

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14. Kuoministers

both ways give you x=3 so its your choice to see which way you liked better.

15. Kuoministers

$\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{green}{\color{blue}T{\color{purple}H{\color{pink}A{\color{red}NK{\color{orange}S}}}}}}}}}}$

16. katlin95

HAHA cool!