Question

ABC ~ XYZ are similar. Find c

Answer 1

The value of
`$c$` is 40

Yes, the triangles in the image are similar.

We know that two triangles are similar if they have the same corresponding angle measures and proportional side lengths. In this case, we can see that the triangles have the same corresponding angle measures:

`* $\angle A = \angle X$`

`* $\angle B = \angle Y$`

We can also see that the corresponding sides of the triangles are proportional:

`* $(AB)/(XY) = (10)/(25) = (2)/(5)$`

`* $(BC)/(YZ) = (16)/(40) = (2)/(5)$`

`* $(CA)/(XZ) = (16)/(40) = (2)/(5)$`

Therefore, the triangles are similar.

To find the value of c, we can use the following proportion:

`$(AB)/(XY) = (BC)/(c)$`

Substituting in the known values, we get:

`$(10)/(25) = (16)/(c)$`

Multiplying both sides by c, we get:

`$10c = 400$`

Dividing both sides by 10, we get:

`$c = 40$`

Therefore, the value of c is 40.