Question

These triangles are similar. Find the missing length, h. 9 x 8 x 9/2. 3 x h x 3/2

Answer 1

`h=(8)/(3)`

Explanation:

We are given the dimensions of two triangles which are similar and we are to find the missing length (h):

Triangle A:
`9 * 8 * (9)/(2)`

Triangle B:
`3 * h * (3)/(2)`

Finding the ratio between the two sides:

`(9)/(3) =3`

`((9)/(2) )/((3)/(2) )=3`

So we can see that the ratio between the side lengths of triangle A to B is 3 so we can write it as:

`3h=8`

`h=(8)/(3)`

Answer 2

8/3

Explanation:

Since the triangles are similar, they have the same angles and aspect. It's just that one is bigger than the other. The sides are all in the same proportions.

So, if the first triangle's sides measure: 9 x 8 x 9/2

and the ones of the second triangle measure: 3 x h x 3/2

We can easily observe that for the two sides we know the dimensions in both triangles, that the second one is 3 times smaller than the first. (3 v 9, 3/2 vs 9/2).

So, we can easily deduce the size of the missing side is also the third of the similar side of the first triangle. So, it goes from 8 to 8/3.