Ask Question
10 February, 22:47

The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet. Find the dimensions of the garden.

+2
Answers (1)
  1. 10 February, 23:04
    0
    1. The information given in the problem is:

    - The length of a rectangular garden is 8 feet longer than the width.

    - The garden is surrounded by a 4-foot sidewalk.

    - The area of the sidewalk is 320 ft ².

    2. So, the length of the rectangular garden is:

    L1=8+W1

    3. The formula for calculate the area of the sidewalk, is:

    A2=L2xW2

    "A2" is the area of the sidewalk (A2=320 ft²).

    "L2" is the length of the sidewalk.

    "W2" is the widht of the sidewalk.

    4. The length of the sidewalk (L2) is:

    L2=L1+4+4 (4 feet on each side)

    L2=L1+8

    5. When you substitute L1=8+W1 into the equation L2=L1+8, you obtain:

    L2=8+W1+8

    L2=W1+16

    6. The widht of the sidewalk is:

    W2=W1+4+4

    W2=W1+8

    7. Now, you must substitute the length and the widht of the sidewalk into the formula A2=L2xW2:

    A2=L2xW2

    A2 = (W1+16) (W1+8)

    320=W1²+16W1+8W1+128

    W1²+16W1+8W1+128-320=0

    W1²+16W1+8W1-192=0

    8. When you solve the quadratic equation, you obtain the value of W1:

    W1=16.97 ft

    9. Finally, you must substitute the value of W1 into the formula L1=8+W1:

    L1=8+W1

    L1=8+16.97

    L1=24.97 ft

    10. Therefore, the dimensions of the garden are:

    L1=24.97 ft

    W1=16.97 ft
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers