Guybrush owns an island monkey preserve which has a length of 2x + 1 units and a width of x – 4 units. if the island is 1,586 square units in size, what are the dimensions of the island?
a.
30 units by 30 units
b.
30 units by 26.5 units
c.
13 units by 122 units
d.
61 units by 26 units

D.  61 units by 26 units

Step-by-step explanation:

To solve this problem, we will simply follow the steps below;

Area = l × w

where l is the length and w is the width

From the question given area = 1586     length = 2x + 1  and w =x -4

We can now proceed to substitute the values into the formula

Area = l×b

1586 = (2x+1)× (x - 4)

Now, we will solve for x

1586 = (2x+1) (x - 4)

Open the bracket

1586 = 2x(x-4) + 1(x-4)

1586 = 2x² - 8x + x - 4

1586 = 2x² - 7x -4

Subtract 1586 from both-side of the equation

1586 -1586   = 2x² - 7x -4- 1586

0 =  2x² - 7x  - 1590

This equation can be rearrange, thus;

2x² - 7x  - 1590 = 0

We can now solve the quadratic equation

using the formula method

x = -b ± √ b² - 4ac    /2a

From the equation above

a = 2         b= -7       and      c=-1590

Substitute the vales into the formula;

x = -(-7) ± √ (-7)² - 4(2)(-1590)     /2(2)

x = 7 ±√ 49+ 12720       /4

x = 7 ±√ 12769    /4

x = 7 ± 113  /4

Either x =       or     x =

Either x =         or     x =

Either  x= 30         or   x=-26.5

There is no such thing as negative length, so we will consider just the positive value.

so ,  x = 30

Length = 2x + 1

We will now substitute x = 30 in  2x + 1

Length = 2x + 1  

              =2(30)  + 1

              =60+1

               =61

Width  =   x - 4

We will substitute x = 30 in  x - 4

width   =  x- 4

            = 30 - 4

           = 26

Therefore the dimensions of the island is 61 units by 26 units

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step-by-step explanation: