BTGmoderatorDC wrote: ↑

Sun Mar 27, 2022 7:15 pm

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

STRATEGY: We have two different ways to solve this question:
Algebraic approach: Assign two variables to the length and width of the original rectangle, then calculate the new dimensions, etc
Assign easy-to-work-with 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