Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

(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.

View image ChanyZ516385
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.