Question

I need help on a geometry question.
How do i find x?

Answer 1

Answer:

Hello.  I hope this helps.

To find x, you need to use the fact that the triangles are similar.  This tells us that ratios between corresponding parts of the triangle are the same.

Here, since the lines on the sides are indicated as parallel, we know that the angle at the bottom left of the diagram is the same as the angle at the top right.  So these angles in the two triangles correspond to each other.

Consequently, the sides of lengths 18 and 27 correspond, as do the altitudes.

So

the ratio between corresponding altitudes = the ratio between corresponding sides

=> x / 16 = 27 / 18

=> x / 16 = 3 / 2

=> x = 3 × 16 / 2

=> x = 3 × 8

=> x = 24