To find the value of \( x \) given that the area of a rectangle is \( 48 , \text{cm}^2 \), with a length of \( (x + 2) \) cm and a width of \( 4 , \text{cm} \), you can use the formula for the area of a rectangle:
\[ \text{Area} = \text{length} \times \text{width} \]
Substituting the given values:
\[ 48 = (x + 2) \times 4 \]
Now, divide both sides by \( 4 \) to isolate \( (x + 2) \):
\[ 12 = x + 2 \]
Next, subtract \( 2 \) from both sides to solve for \( x \):
\[ x = 12 - 2 \] \[ x = 10 \]
Thus, the value of \( x \) is \( 10 \).
To confirm, you can calculate the area with \( x = 10 \):
Length: \( x + 2 = 10 + 2 = 12 \) cm
Width: \( 4 \) cm
Area: \( 12 \times 4 = 48 , \text{cm}^2 \), which matches the given area. Therefore, the solution is correct.
The value of \( x \) is \( 10 \).