Answer
Two angles of the large triangle have equal measurement with that of the small triangle. Therefore, the triangles are identical and their corresponding sides are in proportion. The value of length, \[x=1.25\text{ in}\text{.}\]
Work Step by Step
The figure shows that the large triangle and the small triangle both contain \[90{}^\circ \]angles. They also share a common angle. Thus, two angles of the large triangle have equal measurement with that of the small triangle. Therefore, the triangles are identical and their corresponding sides are proportional.
The side with 4 in. is the perpendicular and is opposite to the common angle in small triangle and 5 in. is the perpendicular and is opposite to the common angle in large triangle. The base is 5 in. small triangle and \[\left( x+5 \right)in.\]in large triangle.
Compute the value of \[x\]as shown below:
\[\begin{align}
& \frac{4}{5}=\frac{5}{x+5} \\
& 4(x+5)=5\times 5 \\
& 4x+20=25 \\
& 4x=25-20
\end{align}\]
\[\begin{align}
& 4x=5 \\
& x=1.25
\end{align}\]
Hence, two angles of the large triangle have equal measurement with that of the small triangle. Therefore, the triangles are identical and their corresponding sides are in proportion. The value of length, \[x=1.25\text{ in}\text{.}\]
