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  3. The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is

The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is

游客2024-01-12  16
问题 The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its length. What is the area of the lawn, in square meters?
选项 A、40.5
B、96
C、108
D、192
E、432
答案 C
解析 Let s and t be the width and length, in meters, of the lawn, respectively. Then the perimeter is 2s + 2t meters, so that 2s + 2t = 42. Also, the relationship between the width and the length can be translated as s = 0.75t. Substituting 0.75t for 5 in the equation for the perimeter yields 42 = 2(0.75t)+ 2t = 3.5t. So t == 12 and s =(0.75)(12)= 9. Since st = 108, the area of the lawn is 108 square meters. The correct answer is Choice C.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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