Word Problems Math Example 2

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Example 2

medium
A rectangular garden has a perimeter of 56 metres. If the length is 3 metres more than twice the width, find the dimensions.

Solution

  1. 1
    Let ww be the width. Then the length is l=2w+3l = 2w + 3.
  2. 2
    Perimeter formula: 2l+2w=562l + 2w = 56, so 2(2w+3)+2w=562(2w + 3) + 2w = 56.
  3. 3
    Expand: 4w+6+2w=564w + 6 + 2w = 56, giving 6w+6=566w + 6 = 56.
  4. 4
    Solve: 6w=506w = 50, so w=506=253โ‰ˆ8.33w = \frac{50}{6} = \frac{25}{3} \approx 8.33 m.
  5. 5
    Length: l=2(253)+3=503+93=593โ‰ˆ19.67l = 2(\frac{25}{3}) + 3 = \frac{50}{3} + \frac{9}{3} = \frac{59}{3} \approx 19.67 m.

Answer

w=253ย m,โ€…โ€Šl=593ย mw = \frac{25}{3} \text{ m},\; l = \frac{59}{3} \text{ m}
Define variables based on the relationships described, set up an equation from the given constraint (perimeter), and solve step by step.

About Word Problems

Word problems require translating a real-world scenario described in natural language into mathematical relationships, identifying the unknown quantity, setting up equations or expressions, and solving them to answer the question.

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