A rectangular garden has a perimeter of 72 m. The length is 4 m more than its width. Find the dimensions of the garden.

Let the length of the rectangular garden be $l$ meters and the width be $w$ meters.
The perimeter of a rectangle is $P = 2(l+w)$.
Half the perimeter is given as 36 m, so:

The length is 4 m more than its width:

Substitute equation $(*2)$ into equation $(*1)$:

Subtract 4 from both sides:

Divide by 2:

Now substitute the value of $w$ back into equation $(*2)$ to find $l$:

The dimensions of the garden are length = 20 m and width = 16 m.

The calculated dimensions are 20 m, 16 m. This matches option (3).

The final answer is $\boxed{\text{20 m, 16 m}}$.

The two linear equations are:

Multiply equation $(*1)$ by 3 and equation $(*2)$ by 2 to make the coefficients of $x$ equal:

Subtract equation $(*4)$ from equation $(*3)$:

Substitute $y=14$ into equation $(*1)$:

Subtract 42 from both sides:

Divide by 2:

The solution is $x=-19, y=14$. This matches option (4).

The final answer is $\boxed{x=-19, y=14}$.

For a quadratic equation in the form $ax^2+bx+c=0$, the roots are real and distinct if the discriminant $\Delta = b^2-4ac$ is greater than 0.

The given equation is $x^2+4x+k=0$.
Here, $a=1$, $b=4$, and $c=k$.
Set the discriminant greater than 0:

Add $4k$ to both sides:

Divide by 4:

This can also be written as $k < 4$.

The condition for real and distinct roots is $k < 4$. Based on the typical structure of such multiple-choice questions, option (3) would represent $k < 4$.

The final answer is $\boxed{k < 4}$.