On a scale drawing of a house, a rectangular bedroom has a length of 8 inches and a perimeter of 30 inches. The scale is 0.5 inch = 1 foot.
What is the actual width in feet of the bedroom?
2L + 2W = perimeter = 30
L+W = 15
If L = 8 , then W = 7
but .5 inches ---> 1 foot or 1 inch ---> 2 feet
so 8 inches ----> .... feet
and 7 inches ---> .... feet
I don't get it?
To find the actual width of the bedroom in feet, we need to use the scale given. The scale states that 0.5 inch on the drawing represents 1 foot in reality.
Step 1: Find the actual length of the bedroom in feet.
Given that the length of the bedroom on the drawing is 8 inches, we need to convert it to feet using the scale. Since 0.5 inch represents 1 foot, we can divide the length by the scale factor:
8 inches รท 0.5 inch = 16 feet
Therefore, the actual length of the bedroom is 16 feet.
Step 2: Find the actual perimeter of the bedroom in feet.
The perimeter of a rectangle is given by the formula: perimeter = 2 * (length + width). We know that the perimeter is 30 inches, so we can substitute the actual length of the bedroom (16 feet) into the formula:
30 inches = 2 * (16 feet + width)
Simplify the equation by dividing both sides by 2 to isolate the expression for the width:
15 inches = 16 feet + width
Step 3: Solve for the width.
Subtract 16 feet from both sides of the equation:
15 inches - 16 feet = width
(Note: In this step, we convert the feet and inches to a common unit, like inches, to make the calculation easier.)
15 inches - (16 feet * 12 inches/1 foot) = width
15 inches - 192 inches = width
-177 inches = width
Therefore, the actual width of the bedroom is -177 inches.
To find the actual width of the rectangular bedroom in feet, we need to first determine the width on the scale drawing.
We know that the scale is 0.5 inch = 1 foot. This means that every 0.5 inch on the scale drawing represents 1 foot in reality.
Given that the length of the bedroom on the scale drawing is 8 inches, we can find its actual length in feet by dividing 8 inches by 0.5 inch/foot:
8 inches / 0.5 inch/foot = 16 feet
Now that we know the actual length of the bedroom is 16 feet, we can use the information given about the bedroom's perimeter to find its width.
The perimeter of a rectangle is given by the formula: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, the perimeter of the bedroom is given as 30 inches. We also know that the length of the bedroom is 8 inches. So we can substitute these values into the formula:
30 inches = 2(8 inches) + 2W
Simplifying,
30 inches = 16 inches + 2W
Subtracting 16 inches from both sides of the equation,
30 inches - 16 inches = 2W
14 inches = 2W
Next, we need to convert the inches into feet using the scale. We know that 1 foot corresponds to 0.5 inch on the scale. So, to convert 14 inches to feet, we divide by 0.5 inch/foot:
14 inches / 0.5 inch/foot = 28 feet
Therefore, the actual width of the bedroom is 28 feet.