Answered

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(b) The diagram below shows the floor plan of a hallway in a theatre. ALI MBATIES shown on the diagram are recorded in metres. Kerw W SIDENT HUB Given that the width, w of the hallway is 12m, find the value of x. Find the length of the hallway, Z. Determine the area of the hallway. Total: 9 marles

B The Diagram Below Shows The Floor Plan Of A Hallway In A Theatre ALI MBATIES Shown On The Diagram Are Recorded In Metres Kerw W SIDENT HUB Given That The Widt class=

Sagot :

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.

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