Find Side Length x+4 in a Square with Area 36

To solve for the side length of the square, we follow these steps:

• Step 1: Given each side of the square as $x+4$ cm, use the area formula for a square: $\text{Area} = (\text{side length})^2$.
• Step 2: Since the area is 36 cm$^2$, set up the equation:

$(x+4)^2 = 36$.

• Step 3: Solve for $x+4$:

Taking the square root of both sides,

$x+4 = 6$ or $x+4 = -6$.

• Step 4: Solve each equation for $x$:
• From $x+4 = 6$, we get $x = 2$.
• From $x+4 = -6$, we get $x = -10$.
• Step 5: Apply the condition $x > -4$:

Only $x = 2$ satisfies the condition $x > -4$.

• Step 6: Calculate the side length using $x = 2$:

Side length = $x+4 = 2+4 = 6$ cm.

Therefore, the length of the sides of the square is $6$ cm.