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Alex Ar [27]
2 years ago
9

Hi algebra is hard please help: The expression (8x+ 4) inches represents the perimeter of a rectangle whose width is (3x − 4) in

ches. Find the length of the rectangle if x = 2
Mathematics
1 answer:
Bess [88]2 years ago
8 0

Answer:

Length = 4 inches

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

If x = 2

Perimeter = 8x - 4

= 8(2) - 4

= 16 - 4

= 12 inches

Width = 3x - 4

= 3(2) - 4

= 6 - 4

= 2 inches

Perimeter of a rectangle = 2(length + width)

12 = 2(length + 2)

12 = 2length + 4

12 - 4 = 2 length

8 = 2 length

Length = 8/2

Length = 4 inches

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For the amount of fencing to be minimum, then

\frac{dP}{dx} =0 \\  \\ \Rightarrow1- \frac{576}{x^2} =0 \\  \\ \Rightarrow \frac{576}{x^2} =1 \\  \\ \Rightarrow x^2=576 \\  \\ \Rightarrow x=\sqrt{576}=24

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Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.
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