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5. GARDEN A 12-foot-by-9-foot fenced area has walking paths along one of the

long sides and one of the short sides with a uniform width x. Flowers are

planted in the remaining part of the enclosed area. The part covered by

flowers is half of the entire enclosed area. What are the dimensions of the

area covered by flowers?



Answer :

oladayoademosu

The dimensions of the area covered by flowers are

  • length = 9 ft and
  • width = 6 ft

How to find the dimensions of the area covered by flowers?

Since the garden is a 12-foot-by-9-foot fenced area has walking paths along one of the long sides and one of the short sides with a uniform width x.

What is the area of the garden?

Since the garden is a rectangle, its area is A = LW where

  • L = length = 12 ft and
  • W = width = 9 ft

So, A = LW

= 12 ft × 9 ft

= 108 ft²

Also, since flowers are planted on the remaining side of the garden with a path of width x on on side, we have that the dimensions of the area covered by flowers is

  • length, L' = 12 - x and
  • width, W' = 9 - x

Since the planted part is rectangle, its area is A' = L'W' where L' 12 - x and W'= 9 - x

So, A' = L'W'

= (12 - x)(9 - x)

Since it is given that he part covered by flowers is half of the entire enclosed area, we have that

A' = A/2

(12 - x)(9 - x) = 108 ft²/2

(12 - x)(9 - x) = 54

Expanding the brackets, we have

108 - 21x + x² = 54

x² - 21x + 108 - 54 = 0

x² - 21x + 54 = 0

Using the quadratic formula, we find x

So, [tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = 1, b = -21 and c = 54

Substituting the values of the variables into the equation, we have

[tex]x = \frac{-(-21) +/- \sqrt{(-21)^{2} - 4\times1\times54} }{2\times1}\\= \frac{21 +/- \sqrt{441 - 216} }{2}\\= \frac{21 +/- \sqrt{225} }{2}\\= \frac{21 +/- 15 }{2}\\= \frac{21 + 15 }{2} or x = \frac{21 - 15 }{2}\\= \frac{36}{2} or x = \frac{6}{2}\\x = 18 or x = 3[/tex]

Since x cannot be greater than the greatest dimension, we choose x = 3.

So,

  • the length, L' = 12 - x = 12 - 3 = 9 ft and
  • the width W' = 9 - x = 9 - 3 = 6 ft

So, the dimensions of the area covered by flowers are

  • length = 9 ft and
  • width = 6 ft

Learn more about dimensions of garden area here:

https://brainly.com/question/8294080

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