An architectural drawing has a scale of 2 in=5 feet. If living room is 15 feet by 18 feet ,what is the living room size . What is the area of the living room in drawing. What is the area of actual. Living room . How do they compare. Using proportion and scale drawing
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Thanks just searched this up and this popped ty damon:)
This worked. Thanks guys.
15 ft * 2 in/ft = 30 in
18 ft * 2 in/ft = 36 in
so area on plan = 30*36 = 1080 in^2
on the real size area = 15*18 = 270 ft^2
well to compare them change in^2 to ft^2
there are 12 in /ft
so 144 in^2 per ft^2
so
1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2
or you could say
30 in = 30/12 ft
36 in = 3 ft
area = 90/12 ft^2 = 7.5 ft^2 luckily :)
To determine the size of the living room in the drawing, we need to use the scale given in the architectural drawing. The scale mentioned is 2 in = 5 feet, which means that 2 inches on the drawing represents 5 feet in real life.
To find the size of the living room in the drawing, we can set up a proportion:
2 inches (drawing) / 5 feet (real life) = x inches (drawing) / 15 feet (real life)
Cross-multiplying, we get:
2 inches * 15 feet = 5 feet * x inches
30 inches = 5x inches
Dividing both sides by 5, we find:
x inches = 6 inches
Therefore, the living room size in the drawing is 6 inches.
To calculate the area of the living room in the drawing, we need to find the length and width of the living room in the drawing. We already know that the length is 6 inches, and to find the width, we need to use the scale again.
Using the same proportion as before, but this time with the width of the living room:
2 inches (drawing) / 5 feet (real life) = y inches (drawing) / 18 feet (real life)
Cross-multiplying, we get:
2 inches * 18 feet = 5 feet * y inches
36 inches = 5y inches
Dividing both sides by 5, we find:
y inches = 7.2 inches (approximate value)
Therefore, the width of the living room in the drawing is approximately 7.2 inches.
Now, we can calculate the area of the living room in the drawing:
Area = length * width
Area = 6 inches * 7.2 inches
Area = 43.2 square inches
To determine the area of the actual living room, we multiply the length and width of the real-life living room:
Area = 15 feet * 18 feet
Area = 270 square feet
Comparing the areas, we find that the area in the drawing is 43.2 square inches, while the area in real life is 270 square feet. These two areas are not directly comparable since they are in different units. To compare them, we can convert the area in real life to square inches using the scale.
Using the same scale mentioned earlier, 2 inches = 5 feet, we can convert the area from square feet to square inches:
Equation: 2 inches (drawing) / 5 feet (real life) = 1 inch (drawing) / x feet (real life)
Since the goal is to convert from square feet to square inches, we square both sides of the equation:
(2 inches / 5 feet)^2 = (1 inch / x feet)^2
(2/5)^2 = 1/x^2
4/25 = 1/x^2
Cross-multiplying, we get:
4x^2 = 25
x^2 = 25/4
x = √(25/4)
x = 5/2 = 2.5
Therefore, 1 inch in the drawing represents 2.5 feet in real life.
Now, we can convert the area of the real-life living room to square inches using the scale:
Area in square inches = Area in square feet * (12 inches / 2.5 feet)^2
Area in square inches = 270 square feet * (12/2.5)^2
Area in square inches = 270 square feet * (4.8)^2
Area in square inches = 270 square feet * 23.04
Area in square inches = 6220.8 square inches
So, the area of the actual living room is approximately 6220.8 square inches.
In summary:
- The living room size in the drawing is 6 inches by 7.2 inches.
- The area of the living room in the drawing is 43.2 square inches.
- The area of the actual living room is approximately 6220.8 square inches.
- The areas are not directly comparable, but by using the scale, we can determine that the area in the drawing is significantly smaller than the area in real life.