Question

6 ft x ft 4 ft 11 ft Which value of x proves that the two triangles above are similar? (G.7)(1 point) O A. 16.5 O B. 6.6 C. 5.5 D. 7.3

Answer 1

We are given two triangles and an unknown side length. We are asked to determine the value of the unknown side in such a way that the two triangles are similar. Let's remember first that two triangles are similar if the corresponding angles are congruent and if corresponding sides are in the same proportion. Since we are given the values of two corresponding sides, we may find the proportion between them by dividing their lengths.

The length of one side is 6, the other length is 10 because is the sum of 6 and 4, therefore, the proportion is:

`(6+4)/(6)=(10)/(6)=(5)/(3)`

Now, this same proportion must work for the other two sides, this means that:

`(11)/(x)=(5)/(3)`

Solving for "x", first by multiplying by "3" on both sides:

`\begin{gathered} ((11)(3))/(x)=5 \\ (33)/(x)=5 \end{gathered}`

now we multiply by "x" on both sides:

`33=5x`

now we divide by "5":

`\begin{gathered} (33)/(5)=x \\ 6.6=x \end{gathered}`

Therefore, for the triangles to be similar "x" must be equal to 6.6