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The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden?

Do not include units in your answer.

User Jarco
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2 Answers

2 votes

Final answer:

To solve for the area of the garden, we first determined the width (46 feet) by solving the perimeter equation, then we found the length by adding 4 feet to the width, resulting in 50 feet. With both dimensions, we calculated the area to be 2300 square feet.

Step-by-step explanation:

To find the area of a rectangular garden where the length is 4 feet longer than the width and the perimeter is 192 feet, we use algebra. Let's define the width of the garden as 'w' feet. Therefore, the length will be 'w + 4' feet. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where 'l' is the length and 'w' is the width. Plugging in the known values, we get 192 = 2(w + 4) + 2w.

Simplifying that equation:

  • 192 = 2w + 8 + 2w
  • 192 = 4w + 8
  • 184 = 4w
  • w = 46 feet

Now that we have the width, we can find the length: l = w + 4 = 46 + 4 = 50 feet.

The area (A) of a rectangle is given by the formula A = l × w. Therefore, the area of the garden is:

  • A = 50 × 46 = 2300 square feet

User CoreTech
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Given : The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden ?

Solution :

Let us assume the breadth be x

The length is 4 ft longer than the Breadth

So, the length be x + 4

Perimeter = 192

❍ Perimeter = 2(Length + Breadth)

  • 192 = 2(x + 4 + x)

  • 192 = 2(2x + 4)

  • 192 = 4x + 8

  • 192 - 8 = 4x

  • 4x = 184

  • x = 46

Length : x + 4 = 46 + 4 = 50

Breadth : x = 46

User YasirPoongadan
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