He must choose the length and breadth of the rose garden as 16.34 feet and 4.34 feet respectively.
What is the area of a rectangle?
The area of a rectangle is the product of the length and the breadth of that rectangle.
Let, the length of the garden is = x feet.
Therefore, breadth of the garden is = (x - 12) feet.
Given,
x(x - 12) = 71
⇒ x² - 12x - 71 = 0
⇒ x = [- (- 12) ± √{(- 12)² - 4 × 1 × (-71)}] / 2 × 1 = [12 ± √{144 + 284}] / 2 = (12 ± √428) / 2 = (12 ± 20.68) / 2
⇒ x = 32.68 / 2
⇒ x = 16.34
We must eliminate the negative value as the length cannot be negative.
Therefore, length of the garden is = 16.34 feet
Hence, breadth of the garden is = (16.34 - 12) feet = 4.34 feet
Learn more about the area of a rectangle here: https://brainly.com/question/8663941
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