Question

Ged test how do I determine the value of x?

Answer 1

D) 26"

1) Similar triangles have proportional sides and congruent angles.

2) As the picture state that these two triangles are similar, then we can write out the following ratios:

`(x)/(8)=(19(1)/(2))/(6)=(32(1)/(2))/(10)`

But notice that, since we have Mixed Numbers it is easier to convert them to Improper fractions:

`\begin{gathered} 32(1)/(2)=(2*32+1)/(2)=(65)/(2) \\ 19(1)/(2)=(2*19+1)/(2)=(39)/(2) \\ \end{gathered}`

To convert it keep the denominator and multiply that by the whole number and then add to the numerator.

2.2) Now we can plug them back, but we just need two ratios the one with the missing length and a ratio with known length:

`\begin{gathered} (x)/(8)=(19(1)/(2))/(6)\Rightarrow(x)/(8)=((39)/(2))/(6) \\ (x)/(8)=((39)/(2))/(6) \\ 6x=8\cdot(39)/(2) \\ 6x=156 \\ (6x)/(6)=(156)/(6) \\ x=26 \end{gathered}`

Hence, the line segment AB is 26inches long