ISEE Word Problems Question 199: Answer and Explanation
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Question: 199
4. If the length of the base of a triangle is decreased by 20 percent and the height of the triangle is increased by 20 percent, what is the percent change in the area of the triangle?
- A. –10%
- B. –4%
- C. 0%
- D. 10%
Correct Answer: B
Explanation:
The answer is B
Let b represent the original base, and let h represent the original height. As area of a triangle is given by 
bh, the original area is bh. As the base was decreased by 20%, the new base will be 80% of the original, or 0.8b. As the height was increased by 20%, the new height will be 120% of the original, or 1.2b. Thus the new area is (0.8b)(1.2h) = 0.48bh, a lower area. Percent change is found by taking the difference, dividing that by the original, and then multiplying the result by 100: 
= 0.04 × 100 = 4%. As the new area