Question

10) The triangles are similar by AA similarity. Solve for x.

A) 1
B) 2
C) 3
D) 4

Answer 1

The answer would be A-1

Answer 2

Answer: x = 1 (option A)

Explanation:

Since we know that the two triangles are similar by AA similarity, we can set up a proportional relationship of the side lengths that we are given to find the missing variable.

The two triangles "share" a base (the side marked '4' and '8'), so we can use these numbers as the numerators in the proportion. The smaller triangle has a base of 8, and the larger triangle's base is 8 units plus the additional 4 units, making its total base length 12 units.

The right triangles' other legs measure 3x + 1 units on the smaller triangle and 6x units on the larger triangle. We can use these side lengths as the denominators in our proportion.

Next, we set up the proportion as follows:

`(8)/(3x+1)=(12)/(6x)`

Then, you can cross-multiply to get the equation:

`48x=36x+12`

After solving down algebraically, the final answer gives us that x is equal to 1, meaning that option A is the correct answer.

I hope this helps!