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

In front of you is a square.

The expressions listed next to the sides describe their length.

( $x>-4$ length measurements in cm).

Since the area of the square is 36.

Find the lengths of the sides of the square.

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.