**A rectangle was altered by increasing its length by 10 percent and decreasing it...**

### Question

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 *?

### Options

The correct answer is C.

### Explanation:

Choice C is correct. Let *l* and *w* be the length and width, respectively of the original rectangle. The area of the original rectangle is A = *lw*. The rectangle is altered by increasing its length by 10 percent and decreasing its width by p percent; thus, the length of the altered rectangle is 1.1*l*, and the width of the altered rectangle is \((1 - \frac{p}{100})w\). The alterations decrease the area by 12 percent, so the area of the altered rectangle is (1 - 0.12)A = 0.88A. The area of the altered rectangle is the product of its length and width, so 0.88A = \((1.1l)(1 - \frac{p}{100})w\). Since A = lw, this last equation can be rewritten as 0.88A = (1.1)\((1 - \frac{p}{100})lw\) = (1.1)\((1 - \frac{p}{100})\)A, from which it follows that 0.88 = (1.1), or 0.8 = (1.1)\((1 - \frac{p}{100})\), or 0.8 = \((1 - \frac{p}{100})\). Therefore,\(\frac{p}{100}\) = 0.2, and so the value of p is 20.

Choice A is incorrect and may be the result of confusing the 12 percent decrease in area with the percent decrease in width. Choice B is incorrect because decreasing the width by 15 percent results in a 6.5 percent decrease in area, not a 12 percent decrease. Choice D is incorrect and may be the result of adding the percents given in the question (10 + 12).

### More Past Questions:

## Discussion

### Other Subjects

- English Language
- Biology
- Mathematics
- Government
- Physics
- Economics
- Chemistry
- Christian Religious Knowledge
- Commerce
- Geography
- Literature In English
- Accounts
- Agricultural Science
- General Paper
- Islamic Religious Knowledge
- History
- Further Mathematics
- Current Affairs
- Civic Education
- Reading
- Writing and Language
- Computer Studies
- Igbo
- French
- Home Economics
- Yoruba
- Hausa
- Fine Arts