Question

I can't post the image yet.
Help will be appreciated
Am i wrong or right i can show image.

A larger rectangle has the side are 3in and the top and bottom of the rectangles are 5in
The smaller rectangle has x sides and the top and bottom has 3in.
Here is what i got.
The figures above are similar. Find the missing length.
Show your work.
The larger rectangle is equal to 16 and the smaller is equal to 8

Answer 1

It's number 6 on this page.

Answer 2

Let's imagine for a moment, that we have two rectangles that are similar:

Where (1) is the big rectangle and (2) is the smaller but similar rectangle.
Since they are similar, it means that every measure of rectangle (1) is proportional to the measure of the sides that compose recangle (2).
What does that imply?.
The answer is: a constant.

This constant is denominated "coefficient of proportionality" and it pretty much represents the number you have to multiply the small rectangle's sides (in this case rectangle (2)) to obtain the measures of the bigger rectangle (in this case, (1)).
So, therefore, we represent it, as a mathematical expression:
\[a=k.y\]
\[b=k.x\]
The strategy wold be to find that "k" of the triangles and then the unknown sides of both triangles become evident.

So, applying it to your problem:

And we are given that the triangles are similar, so therefore, we can just use the whole concept I described to you and represent it as a proportion:
\[5=k.3\]
\[3=k.x\]
So, all you have to do now is find the value of "k" using the first equation, then replace it in the second and solve it for "x", and you will solve the problem that way.