similar triangles I think. and I need help with this

[bamba12312]

so ABCD is a square and every side is 6 and we need to mark LK as X and we need to find them with X the height of square LEK I think there is similar triangles LEK and DEC because DC and LK are parallel sides so that means that angle L equal angle D and angle K equal angle C and I don't know how to find the hight using X
the answer is

 

[blamocur]

View attachment 33758
so ABCD is a square and every side is 6 and we need to mark LK as X and we need to find them with X the height of square LEK I think there is similar triangles LEK and DEC because DC and LK are parallel sides so that means that angle L equal angle D and angle K equal angle C and I don't know how to find the hight using X
the answer isView attachment 33760

I agree with you about similar triangles. My next step would be to use this similarity in order to write an equation for the height of LEK.

 

[Deleted member 4993]

View attachment 33758
so ABCD is a square and every side is 6 and we need to mark LK as X and we need to find them with X the height of square LEK I think there is similar triangles LEK and DEC because DC and LK are parallel sides so that means that angle L equal angle D and angle K equal angle C and I don't know how to find the hight using X
the answer isView attachment 33760

You write:

"..........and we need to find them with X the height of square LEK"

What do you mean by them?

When you write "square LEK" - did you mean triangle LEK ?

 

[bamba12312]

You write:

"..........and we need to find them with X the height of square LEK"

What do you mean by them?

When you write "square LEK" - did you mean triangle LEK ?

yes my English is really poor I am sorry for that

 

[bamba12312]

I agree with you about similar triangles. My next step would be to use this similarity in order to write an equation for the height of LEK.

I don't really understand how to do that

 

[Dr.Peterson]

yes my English is really poor I am sorry for that

I think this is what you meant:

View attachment 33758
so ABCD is a square and every side is 6 and we need to mark LK as X and we need to find them with X the height of square LEK I think there is similar triangles LEK and DEC because DC and LK are parallel sides so that means that angle L equal angle D and angle K equal angle C and I don't know how to find the hight using X
the answer isView attachment 33760

Change "we need to find them with X the height of square LEK" to "we need to find the height of triangle LEK in terms of X". That is, you are to write an expression for this height using the variable X.

I don't really understand how to do that [use similarity]

Draw in the height of both triangles:



Then write a proportion using the similarity.

 

[JeffM]

I don't really understand how to do that

The point about similar triangles is that (1) the measure of any angle in one of the triangles equals the measure of the corresponding angle in the other triangle, and (2) the ratios of any corresponding lengths in the two triangles are identical. So, for example, once you know that triangles DEC and LEK are similar, you also know that

$$\dfrac{\text {linear measure of base of } \triangle DEC}{\text {linear measure of base of } \triangle LEK} = \dfrac{\text {linear measure of height of } \triangle DEC}{\text {linear measure of height of } \triangle LEK}.$$
With me to here?

Now, the linear measure of the bases are 6 and x respectively, but you do not know what the two heights are. Let’s name them. We say height of DEC is p, and height of LEK is q.

Can we figure out anything about the numerical relationship between those two heights? (A picture will help.)

Yes, we can, namely $p = q + 6.$

How did we determine that, pray tell?

Therefore, $\dfrac{6}{x} = \dfrac{p}{q} = \dfrac{q + 6}{q}.$

Now solve for q.

 

[bamba12312]

I don't understand how to solve for q the answer includes q in it

 

[Deleted member 4993]

"..........and we need to find them with X the height of square LEK"

What do you mean by them?

You did not answer the question above.

 

[Dr.Peterson]

I don't understand how to solve for q the answer includes q in it

You need to solve for JeffM's q (my h) in terms of x; that is, the answer contains the variable x. So rearrange this to isolate q:
$$\dfrac{6}{x} = \dfrac{q + 6}{q}$$
But also be sure to tell us whether you understand where that equation came from.

You did not answer the question above [What do you mean by them?].

I think I answered that in my restatement, though it would be good to have confirmation:

"we need to find the height of triangle LEK in terms of X"

"Them" is just an inappropriate grammatical insertion, possibly representing how this would be said in their native language. It would basically be a stand-in for "the height" which is mentioned later.