Multiple choice

A rectangle was altered by increasing its length by $10$ percent and decreasing its width by $p$ percent. If these alterations decreased the area of the rectangle by $12$ percent, what is the value of $p$?

  1. $12$
  2. $15$
  3. $20$
  4. $22$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original area = L*W. New area = 1.1L * (1-p/100)W = 0.88LW. 1.1 * (1-p/100) = 0.88. 1-p/100 = 0.88/1.1 = 0.8. p/100 = 0.2, so p = 20.

AI explanation

The area of the rectangle changes by a factor of 1.10 for the length and (1 - p/100) for the width, resulting in a net area of 88% of the original. This relationship gives the equation (1.10)(1 - p/100) = 0.88. Solving for the width factor yields (1 - p/100) = 0.80, which means p equals 20.

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