Question

The length and width of a rectangle are shown below.

A rectangle with a length of 2-x plus 10 and a width of 50 minus x.

Which expression represents the area, in square units, of the rectangle?

Answer 1

To find the area of a rectangle, you multiply the length by the width.

Given:
- Length \( L = (2 - x) + 10 = 12 - x \)
- Width \( W = 50 - x \)

Now, we can express the area \( A \) of the rectangle as:

\[
A = L \times W
\]

Substituting the expressions for length and width, we have:

\[
A = (12 - x)(50 - x)
\]

Now, we can expand this expression:

\[
A = 12 \cdot 50 - 12x - x \cdot 50 + x^2
\]
\[
A = 600 - 12x - 50x + x^2
\]
\[
A = 600 - 62x + x^2
\]

So, the expression that represents the area of the rectangle is:

\[
A = x^2 - 62x + 600
\]

This is the expression for the area in square units.