Let's define the dimensions of the rectangular classroom.
Let:
- \( W \) be the width of the classroom.
- The length \( L \) of the classroom is given by: \[ L = W - 6 \] (since the length is six feet shorter than the width).
If Mrs. Lordes wants to increase both dimensions by \( x \) feet, the new width and length will be:
- New Width: \( W + x \)
- New Length: \( (W - 6) + x = W + x - 6 \)
The area \( N \) of the new rectangle can be expressed as: \[ N = \text{New Width} \times \text{New Length} \] Substituting in the expressions for the new dimensions: \[ N = (W + x) \times (W + x - 6) \]
Now, expanding this equation: \[ N = (W + x)(W + x - 6) = (W + x)(W + x) - 6(W + x) = (W + x)^2 - 6(W + x) \]
So, the equation that represents the new area \( N \) is: \[ N = (W + x)^2 - 6(W + x) \]
That's the general form of the equation representing the new area after increasing the dimensions by \( x \) feet.
1 answer