the perimeter of the room is 16yd and the area is 16yd^2. What would the perimeter and the area of the room be in a scale drawing:
1ft to 4yd
please help i don't get this at all!!!
Since each side of the room is 4 yards, then each side of the room would be 1 foot on a scale drawing.
i still am confused?? what do i do???
The perimeter on the scale drawing would be 1 ft. + 1 ft. + 1 ft. + 1 ft. = ? ft
The area would be 1 ft. * 1 ft. = ? ft.
oh ok thanks!
You're welcome. :-)
To find the perimeter and area of the room in the scale drawing, we first need to convert the dimensions from yards to feet using the given scale of 1ft to 4yd.
Let's start with the perimeter. The perimeter of a rectangle is the sum of all its sides. In this case, the given perimeter is 16 yards.
To convert yards to feet, we need to multiply the given value by the conversion factor: 1 yard = 3 feet. Therefore, 16 yards is equal to 16 x 3 = 48 feet.
Now we can apply the scale ratio of 1ft to 4yd. Since 1 yard is equal to 3 feet, we can say that 4 yards is equal to 4 x 3 = 12 feet. Therefore, the scaled perimeter in the drawing would be 48 feet ÷ 12 feet per yard = 4 yards.
Next, let's calculate the area. The area of a rectangle is found by multiplying the length by the width. In this case, the given area is 16 square yards.
Using the scale ratio, we need to convert the area from square yards to square feet. Since 1 yard is equal to 3 feet, 1 square yard is equal to (1 x 3) x (1 x 3) = 9 square feet. Therefore, 16 square yards is equal to 16 x 9 = 144 square feet.
To find the dimensions in the scaled drawing, we need to find the length and width of the room. Using the given area, we can set up an equation: length x width = 144 square feet.
Since the room is a rectangle, we know that the perimeter is twice the sum of the length and width. In other words, perimeter = 2(length + width).
We have two equations:
1) length x width = 144 square feet
2) 2(length + width) = 4 yards
By substituting the scale factor (4 yards) in the second equation, we can solve for the perimeter.
Let's consider different possibilities for length and width to fulfill these equations:
- If length = 12 feet and width = 12 feet, the area is 12 x 12 = 144 square feet, which satisfies equation (1).
- The perimeter is then 2(12 + 12) = 48 feet. Converting this to yards by dividing by 3, we get 48 feet ÷ 3 feet per yard = 16 yards. This also satisfies equation (2).
So, in the scale drawing, the perimeter would be 16 yards, and the area would be 16 square yards.