A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle?
Are you positive this is correct?
To find the change in the area of the rectangle, we need to calculate the original area and the new area after the changes in length and width.
Step 1: Calculate the original area of the rectangle.
The original area is given by the formula:
Area = Length x Width
Substituting the given values:
Area = 12 ft x 5 ft
Area = 60 square ft
Step 2: Calculate the new dimensions of the rectangle.
To find the new length and width after the changes, we can use the following formulas:
New Length = Original Length + (Change Percent/100) x Original Length
New Width = Original Width - (Change Percent/100) x Original Width
Substituting the given values:
New Length = 12 ft + (25/100) x 12 ft
New Length = 12 ft + 3 ft
New Length = 15 ft
New Width = 5 ft - (20/100) x 5 ft
New Width = 5 ft - 1 ft
New Width = 4 ft
Step 3: Calculate the new area of the rectangle.
Using the new length and width, we can calculate the new area using the formula:
New Area = New Length x New Width
Substituting the calculated values:
New Area = 15 ft x 4 ft
New Area = 60 square ft
Step 4: Calculate the change in the area.
Change in Area = New Area - Original Area
Substituting the calculated values:
Change in Area = 60 square ft - 60 square ft
Change in Area = 0 square ft
Therefore, the change in the area of the rectangle is 0 square feet.
To find the change in the area of the rectangle, we first need to calculate the original area and then calculate the new area.
The formula for the area of a rectangle is length multiplied by width.
Given that the original length is 12 feet and the original width is 5 feet, the original area can be calculated as:
Original area = original length * original width
= 12 feet * 5 feet
= 60 square feet
To calculate the new length, we increase the original length by 25%. To find the increase, we multiply the original length by 25% and add it to the original length.
Increase in length = original length * increase percentage
= 12 feet * 25%
= 12 feet * (25/100)
= 3 feet
New length = original length + increase in length
= 12 feet + 3 feet
= 15 feet
Similarly, to calculate the new width, we decrease the original width by 20%. To find the decrease, we multiply the original width by 20% and subtract it from the original width.
Decrease in width = original width * decrease percentage
= 5 feet * 20%
= 5 feet * (20/100)
= 1 foot
New width = original width - decrease in width
= 5 feet - 1 foot
= 4 feet
To find the new area, we multiply the new length by the new width.
New area = new length * new width
= 15 feet * 4 feet
= 60 square feet
Finally, to find the change in the area, we subtract the original area from the new area.
Change in area = new area - original area
= 60 square feet - 60 square feet
= 0 square feet
Therefore, the change in the area of the rectangle is 0 square feet.
The old area is 12*5=60
the new area is
12*1.25 * 5*1.20 = 90
So, the increase is 90-60 = 30
As for % increase, note that you now have
12*1.25 * 5*1.20 = (12*5)(1.25 * 1.20) = (12*5)(1.50)
That is a 50% increase