A rectangular garden has a length that is 5 feet longer than its width. If the area of the garden is 100 square feet, find the dimensions (length and width) of the garden.
Guide On Rating System
Vote
Let the width of the garden be x feet.
The length of the garden is then x + 5 feet.
The area of the garden is the product of the length and the width, so we have:
x(x + 5) = 100
Simplifying the equation, we get:
x^2 + 5x = 100
Rearranging the terms, we have:
x^2 + 5x - 100 = 0
Applying the quadratic formula, we get:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 5, and c = -100.
Substituting these values into the quadratic formula, we have:
x = (-5 ± √(5^2 - 4(1)(-100))) / (2(1))
x = (-5 ± √(25 + 400)) / 2
x = (-5 ± √(425)) / 2
Since the dimensions of a garden cannot be negative, we discard the negative value and take only the positive value.
x = (-5 + √425) / 2
x ≈ 7.87
Therefore, the width of the garden is approximately 7.87 feet.
The length of the garden is then x + 5 = 7.87 + 5 = 12.87 feet (approximately).
Therefore, the dimensions of the garden are approximately 7.87 feet by 12.87 feet.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99