(99 POINTS) Using similarity solve for x. Show all work

Accepted Solution

Hey there! :D

The biggest thing to remember here is the similar triangles and their side lengths. 

Okay, so we can separate these triangles into 3 similar triangles. Which, we only need to do that to two for a proportion, but if you were to have more variables, you could separate the triangles even more if you needed to. 

We want to find two triangles that have "x" has a value of their side, so we can solve a proportion. 

The bigger triangle, (the whole two triangles combine) and the smaller triangle on the left can be used to make a proportion.

On the smaller triangle:

We have 9 cm on the shorter side and x as the hypotenuse. 

On the larger triangle: 

We have x as the shorter side, and then 25 as the hypotenuse. (9+16)

Note: You have to flip the larger triangle upside down to make it a similar structure to the other two triangles. It is similar, you just have to flip it. 

So, now we can make a proportion. 

[tex] \frac{x}{9} = \frac{25}{x} [/tex]

Now, cross multiply. 

9*25= 225

x*x= [tex] x^{2} [/tex]

So, find the square root. 

√225= 15

x= 15. 

I hope this helps!