Question

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.

Answer 1

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

$L+2W=40$

now, we can solve for L

$L=40-2W$

we know that

area of rectangle is

$A=L*W$

$100=L*W$

now, we can plug

$100=(40-2W)*W$

now, we can solve for W

$-2W^2+40W-100=0$

we can use quadratic formula

$W=\frac{-40+\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}$

$W=\frac{-40-\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}$

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

first dimensions:

$W=2.929$

now, we can find L

$L=40-2*2.929$

$L=34.142$

so, length is 34.142feet

width is 2.929 feet

Second dimensions:

$W=17.071$

now, we can find L

$L=40-2*17.071$

$L=5.858$

so, length is 5.858feet

width is 17.071 feet