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:

$\frac{27}{12}=\frac{12}{x}$

Reversing the fractions:

$\frac{12}{27}=\frac{x}{12}$

Multiplying both sides by 12:

$\frac{12\cdot12}{27}=x$

Multiplying numbers and simplifying:

$\frac{16}{3}=x$

The answer is the option D: 16/3