If the length of a rectangle is decreased by 10% and its width is decreased by 20%, by what percent does its area decrease?
A. 30%
B. 28%
C. 25%
D. 23%
E. 15%
OA B
Source: Princeton Review
If the length of a rectangle is decreased by 10% and its width is decreased by 20%, by what percent does its area
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STRATEGY: We have two different ways to solve this question:BTGmoderatorDC wrote: ↑Sun Mar 27, 2022 7:15 pmIf the length of a rectangle is decreased by 10% and its width is decreased by 20%, by what percent does its area decrease?
A. 30%
B. 28%
C. 25%
D. 23%
E. 15%
OA B
Source: Princeton Review
Algebraic approach: Assign two variables to the length and width of the original rectangle, then calculate the new dimensions, etc
Assign easytoworkwith values to the length and width.
Let's use the second approach (since it's easier)
Let 10 = the length of the original rectangle
Let 10 = the width of the original rectangle
Aside: Some students assert that these measurements are those of a square, not a rectangle. However, it's important to remember that a square is just a special kind of rectangle (in the same way that a square is a special kind of rhombus). So these measurements are perfectly fine.
Area of the ORIGINAL rectangle = (base)(width) = (10)(10) = 100
The length of a rectangle is decreased by 10% and its width is decreased by 20%
NEW length of the rectangle = 10  (10% of 10) = 10  1 = 9
NEW width of the rectangle = 10  (20% of 10) = 10  2 = 8
Area of the NEW rectangle = (base)(width) = (9)(8) = 72
So, the area decreased from 100 to 72
Percent decrease = 100(old  new)/old = (100)(100  72)/100 = (100)(28)/100 = 28%
Answer: B
Area of rectangle \(=\) length * breadthBTGmoderatorDC wrote: ↑Sun Mar 27, 2022 7:15 pmIf the length of a rectangle is decreased by 10% and its width is decreased by 20%, by what percent does its area decrease?
A. 30%
B. 28%
C. 25%
D. 23%
E. 15%
OA B
Source: Princeton Review
Area \(= l*b\)
New length \(=0.9 l\)
New breadth \(=0.8 b\)
New area \(= 0.9l *0.8 b = 0.72 l*b\)
Hence its a \(28\%\) decrease
Therefore, B