Respuesta :
Answer:
length = 26.6
width = 11.3
Step-by-step explanation:
1. Set up the equation
(2x + 4)(x) = 300
2. Simplify
2x² + 4x = 300
3. Solve by completing the square
Divide by 2 to make "a" equal to 1
x² + 2x = 150
Find term to complete the square by squaring half of "b"
(2/2)² = 1
x² + 2x + 1 = 150 + 1
Factor perfect square trinomial
√x² + 2x + √1 = 151
(x+1)² = 151
Square root each side
x + 1 = ±12.3
Set up two possibilities and solve
x + 1 = 12.3
x = 11.3
x + 1 = -12.3
x = -13.3
The measurement cannot be negative so width is equal to 11.3
4. Use the width to solve for the length
11.3(2) + 4 = 26.6
The length and width is 26.6 and 11.3.
Calculation of the length and width:
Since The length of the fence is four more than two times the width.
So here the equation should be
(2x + 4)(x) = 300
[tex]2x^2 + 4x = 300[/tex]
Now
Here we divided by 2
So,
[tex]x^2 + 2x = 150[/tex]
Now we determine the term
[tex](2/2)^2 = 1\\\\x^2 + 2x + 1 = 150 + 1[/tex]
Now applied the Factor perfect square trinomial
[tex]\sqrt x^2 + 2x + \sqrt1 = 151\\\(x+1)^2 = 151[/tex]
Now do the Square root each side
x + 1 = ±12.3
Here we required to set up two possibilities and solve
x + 1 = 12.3
x = 11.3
And,
x + 1 = -12.3
x = -13.3
The measurement should not be negative so the width is equal to 11.3
Now the width is
= 11.3(2) + 4
= 26.6
Therefore, The length and width is 26.6 and 11.3.
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