What is the value of x?

Question

louisa_carrillo · Answer

davejavous · Answer

Can you see that the angles marked tell us that the triangles are similar - that is - they're the same triangle but just "zoomed in"?

louisa_carrillo · Answer

I know but, I just need to find out what x is and I've tried everything but my teacher keeps saying that I'm wrong

shadowlegendx · Answer

Since these triangles fulfill the criterion of being similar triangles, via AA( or Angle Angle) as you can see in the image, by the notations made in both angles depicting that they are congruent.

shadowlegendx · Answer

We can then solve for x, using a method for similar triangles

shadowlegendx · Answer

You have to compare the sides, essentially

shadowlegendx · Answer

Does that sound familiar?

louisa_carrillo · Answer

Yes.

shadowlegendx · Answer

Do you know how we would set it up?

louisa_carrillo · Answer

No....

louisa_carrillo · Answer

I know that if I add 5 to the 25 it would equal the 30....

louisa_carrillo · Answer

And they are the same side of the angles

shadowlegendx · Answer

We can't solve for it like that.

shadowlegendx · Answer

What you do, is you compare the one side of triangle KJL to it's counterpart side on triangle NMP. Does that make sense?

louisa_carrillo · Answer

Yes

shadowlegendx · Answer

Lets begin,

Compare side KJ to side NM
$$\frac{ 25 }{ 30 }$$

Compare side JL to MP 
$$\frac{ 20 }{ 4x-4 }$$

shadowlegendx · Answer

KJ over NM

JL over MP

shadowlegendx · Answer

Now lets make an equation

$$\frac{ 25 }{ 30 } = \frac{ 20 }{ 4x - 4 }$$

shadowlegendx · Answer

Lets solve for x :)

louisa_carrillo · Answer

do I use cross division ?

shadowlegendx · Answer

$$25(4x-4) = 30(20)$$

Distribute

$$100x - 100 = 600$$

Add 100 to both sides

$$100x =700$$

Divide both sides by 100

$$x = 7$$

shadowlegendx · Answer

Cross multiply, not cross division

louisa_carrillo · Answer

Oh ok I get it now thank you!

shadowlegendx · Answer

If you ever want to test if you were correct, just input x into the equation

$$\frac{ 25 }{ 30 } =  \frac{ 20 }{ 4(7) - 4} \rightarrow \frac{ 25 }{ 30  } = \frac{ 20 }{ 28-4 }$$

$$\frac{ 25 }{ 30 } = \frac{ 20 }{ 24 }$$

shadowlegendx · Answer

Input the fractions into a calculator, you would get the same decimal

shadowlegendx · Answer

Which is = 0.83333333333

shadowlegendx · Answer

Which means they are equal to each other, therefore the equation is true, and we are correct

shadowlegendx · Answer

Let me know if you have any questions