Question

A rectangular classroom has a length that is six feet shorter than its width,
. Mrs. Lordes wants to increase both dimensions by
feet.

The equation that represents the new area,
N, is

Answer 1

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.