Eric wants to create a scale drawing of a house. The house is 60 feet long and 40 feet wide. The scale drawing needs to fit on a piece of paper that is 6 inches wide. The drawing itself must be at least 3 inches wide. If the new width is 4 inches. How many inches would the new length be? Enter only the numerical information with no label.
AAAaannndd the bot gets it wrong yet again!
the scale is 4in:40 ft = 1in:10ft
so the scaled length will be 6in to represent 60ft
To find the new length of the scale drawing, we can use proportions. Proportions help us solve problems where two ratios are equal.
First, we need to determine the scale factor, which is the ratio of the width of the actual house to the width of the scale drawing.
The actual width of the house is 40 feet, and the width of the scale drawing is 4 inches. To convert feet to inches, we multiply by 12 since there are 12 inches in a foot.
So, the proportion would be:
40 feet / 4 inches = 60 feet / x inches
To simplify this equation, we convert feet to inches:
40 feet * 12 inches/foot = 480 inches
60 feet * 12 inches/foot = 720 inches
Now we can rewrite the proportion:
480 inches / 4 inches = 720 inches / x inches
To solve for x (the new length of the scale drawing), we cross-multiply:
480 inches * x inches = 4 inches * 720 inches
Next, we divide both sides of the equation by 480 inches to isolate x:
x inches = (4 inches * 720 inches) / 480 inches
Finally, we can simplify and calculate:
x inches = 2880 inches / 480 inches
x inches = 6
Therefore, the new length of the scale drawing would be 6 inches.
6:60 = 1:10 (scale factor for length)
Let x be the new length.
1:10 = 3:x-3 (scale factor for width)
Solving for x, we get:
1/10 = 3/(x-3)
3x - 9 = 10
3x = 19
x = 6.33 inches (rounded to two decimal places)
Therefore, the new length would be 6.33 inches.
Apologies for the error in the previous response. You are correct that the scale is 4in:40ft = 1in:10ft. Therefore, the scaled length will be 6in to represent 60ft.
Using the same scale, we can find the width of the scale drawing as:
1in:10ft = 3:x
Cross-multiplying, we get:
1x = 30
x = 30 inches
However, since the drawing itself must be at least 3 inches wide, the new width is given as 4 inches. Therefore, the actual scale used is:
4in:30in = 1in:7.5in
Using this scale, we can find the new length as:
1in:10ft = x:7.5in
Cross-multiplying, we get:
10x = 75
x = 7.5 feet
Therefore, the new length would be 7.5 feet or 90 inches.