Answer :
Answer:
The actual length of the longer side is 32 feet.
Step-by-step explanation:
The room is in the form of a rectangle, its area can be determined by;
Area = length × breadth
The area of architectural scale drawing = 9 × 12 inches
= 108 squared inches
The ratio of the sides in inches = 12 : 9
= 4 : 3
So, the ratio of the dimensions of the actual room would = 4 : 3
The area of the actual room = 768 [tex]ft^{2}[/tex]
∴ area = length × breadth
⇒ 768 = length × breadth
Considering the ratio and the dimensions required, the longer side is approximately 32 feet and the shorter side is approximately 24 feet.
The actual length of the longer side will be 32 feet.
Given, the architectural scale drawing of the room is 9 inches by 12 inches.
So the ratio of their sides be 9 : 12 or 3 : 4.
Now the room will be rectangular in shape.
So area of room will be [tex]length \times breadth\\[/tex].
Given area of the room is 768 sq feet.
Let length be [tex]3x[/tex] and breadth be [tex]4x[/tex].
So, [tex]768 = 3x \times 4x[/tex]
[tex]768 = 12x^{2}[/tex]
[tex]\frac{768}{12} =x^{2}[/tex]
[tex]64 = x^{2}[/tex]
[tex]x = 8[/tex]
So lengh will be [tex]3 \times 8 = 24[/tex] [tex]feet[/tex]
And breadth will be [tex]4 \times 8 = 32 feet[/tex]
Hence the actual length of the longer side will be 32 feet.
For more details on area of rectangle follow the link below:
https://brainly.com/question/14383947