Question

(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

Answer 1

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.

Step-by-step explanation:

1) From, the figure

`\begin{gathered} w=2x+x \\ 12=3x \\ x=(12)/(3) \\ x=4m \end{gathered}`

2) The length of the hallway is,

`\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}`

Then,

`\begin{gathered} x^2+b^2=5^2 \\ 4^2+b^2=25 \\ b^2=25-16 \\ b^2=9 \\ b=3m \end{gathered}`

Therefore, the length of the hallway is,

`\begin{gathered} Length,l=14+9 \\ l=23m \end{gathered}`

3) The area of the hallway is,

`\begin{gathered} Area=x* w+10* x+(1)/(2)* b* x \\ =4*12+10*4+(1)/(2)*9*4 \\ =48+40+18 \\ =106m^2 \end{gathered}`

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.