Given:
In a larger right triangle,
Base, 28ft
Height, x
In a smaller right triangle,
Base, 8ft
Height, 5ft 6inches
In foot,
[tex]\begin{gathered} 5+6(\frac{1}{12})=5+0.5[Since,1\text{ inches =}\frac{1}{12}foot] \\ =5.5ft \end{gathered}[/tex]To find:
The similarity postulate and the value of x
Explanation:
From the diagram, we observe that,
There is a pair of congruent right angles and a pair of congruent angles.
Therefore, by using the AA postulate,
The given two triangles are similar triangles.
So, the corresponding sides are proportional.
Therefore, we write
[tex]\begin{gathered} \frac{x}{5.5}=\frac{28}{8} \\ x=\frac{28\times5.5}{8} \\ x=19.25ft \end{gathered}[/tex]Therefore, the value of x is 19.25 ft.
Final answer: Option C
There is a pair of congruent right angles and a pair of congruent angles. so the triangles are similar by the AA postulate.
The value of x is 19.25 ft.