ISEE Word Problems Question 203: Answer and Explanation
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Question: 203
1. A rectangle has an area of 88 cm2. If the base and height are measured in whole centimeters, what is the greatest possible perimeter of the rectangle?
- A. 38 cm
- B. 92 cm
- C. 178 cm
- D. 264 cm
Correct Answer: C
Explanation:
The answer is C
The greatest perimeter of a rectangle with a given area will have the greatest difference between the length and the width. As the area is 88 and the sides are integers, the greatest difference is created if the length is 88 and the height is 1. Thus, the perimeter is 178.
Guess and check. If the sides are 11 and 8, the perimeter is 38. Now try another set, such as 44 and 2. Now the perimeter is 92. As you flatten the rectangle, the peri-meter grows. Now try 88 and 1. This yields 178. There are no other integer values available to further flatten the rectangle.