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You plant a rectangular rose garden along the side of your garage. You enclose 3 sides of the garden with 40 feet of fencing. The total area of the garden is 100 square feet. Find the possible dimensions of the garden.

Respuesta :

Let's assume

length of rectangle =L

width of rectangle =W

You enclose 3 sides of the garden with 40 feet of fencing

so, we get

[tex]L+2W=40[/tex]

now, we can solve for L

[tex]L=40-2W[/tex]

we know that

area of rectangle is

[tex]A=L*W[/tex]

[tex]100=L*W[/tex]

now, we can plug

[tex]100=(40-2W)*W[/tex]

now, we can solve for W

[tex]-2W^2+40W-100=0[/tex]

we can use quadratic formula

[tex]W=\frac{-40+\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}[/tex]

[tex]W=\frac{-40-\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}[/tex]

we can take anyone value ..because both are giving positive value

first dimensions:

[tex]W=2.929[/tex]

now, we can find L

[tex]L=40-2*2.929[/tex]

[tex]L=34.142[/tex]

so, length is 34.142feet

width is 2.929 feet

Second dimensions:

[tex]W=17.071[/tex]

now, we can find L

[tex]L=40-2*17.071[/tex]

[tex]L=5.858[/tex]

so, length is 5.858feet

width is 17.071 feet



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