Given
The width of the hallway is 12m.
To find:
1) The value of x.
2) The length of the hallway, l.
3) Determine the area of the hallway.
Explanation:
1) From, the figure
[tex]\begin{gathered} w=2x+x \\ 12=3x \\ x=\frac{12}{3} \\ x=4m \end{gathered}[/tex]
2) The length of the hallway is,
[tex]\begin{gathered} Length,l=x+10+b \\ l=4+10+b \\ l=14+b \\ where\text{ }b\text{ }is\text{ the base of the triangle.} \end{gathered}[/tex]
Then,
[tex]\begin{gathered} x^2+b^2=5^2 \\ 4^2+b^2=25 \\ b^2=25-16 \\ b^2=9 \\ b=3m \end{gathered}[/tex]
Therefore, the length of the hallway is,
[tex]\begin{gathered} Length,l=14+9 \\ l=23m \end{gathered}[/tex]
3) The area of the hallway is,
[tex]\begin{gathered} Area=x\times w+10\times x+\frac{1}{2}\times b\times x \\ =4\times12+10\times4+\frac{1}{2}\times9\times4 \\ =48+40+18 \\ =106m^2 \end{gathered}[/tex]
Hence, the answers are,
1) The value of x is 4m.
2) The length of the hallway is 23m.
3) The area of the hallway is 106m^2.
