Question

What is the value of x in the figure below? In this diagram, AABD ~ ACAD.

A. 27
B. 1324
C. 127
D. 16 over 3
E. 6
F. 27 over 12

Answer 1

EXPLANATION

We can apply the Triangle Similarity Theorem in order to get the value of x as shown as follows:

`\frac{\text{Hypotenuse}_{\text{outer}}}{\text{Hypotenuse\_inner}}=\frac{\text{adjacent outer}}{\text{adjacent inner}}`

Replacing terms:

`(27)/(12)=(12)/(x)`

Reversing the fractions:

`(12)/(27)=(x)/(12)`

Multiplying both sides by 12:

`(12\cdot12)/(27)=x`

Multiplying numbers and simplifying:

`(16)/(3)=x`

The answer is the option D: 16/3