题目
The length and width of a painted rectangle were each increased by 10%.
Quantity A
The percent increase in the area of the painted rectangle
选项
A.The quantity in Column A is greater.
B.The quantity in Column B is greater.
C.The two quantities are equal.
D.The relationship cannot be determined from the information given.
解析
为矩形的边长选取便于计算的数值——例如,长=20,宽=10。
矩形的原始面积=长×宽=200。长和宽均增加10%后,面积变为22×11=242。
使用百分比变化公式:
百分比变化 = $\frac{\text{变化量}}{\text{原值}} \times 100\% = \frac{242-200}{200} \times 100\% = 21\%$
A项的数值更大。
也可通过逻辑分析:面积公式为长×宽。若仅一条边增加10%,总面积将增加10%;若两条边均增加10%,总面积的增幅将超过10%。