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?
A.
B.
C.
D.
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?
A.
B.
C.
D.
Answers
GPT-4o mini
To find the area of a rectangle, you multiply its length by its width. In your case, the length of the rectangle is \( (2 - x) + 10 \) and the width is \( 50 - x \).
First, let's simplify the expression for the length:
\[
\text{Length} = (2 - x) + 10 = 12 - x
\]
Now, we have:
- Length: \( 12 - x \)
- Width: \( 50 - x \)
Next, we can calculate the area \( A \) of the rectangle:
\[
A = \text{Length} \times \text{Width} = (12 - x)(50 - x)
\]
Now, we can expand this expression using the distributive property (also known as the FOIL method for binomials):
\[
A = (12)(50) + (12)(-x) + (-x)(50) + (-x)(-x)
\]
Calculating each term:
1. \( 12 \times 50 = 600 \)
2. \( 12 \times -x = -12x \)
3. \( -x \times 50 = -50x \)
4. \( -x \times -x = x^2 \)
Combining these results, we get:
\[
A = 600 - 12x - 50x + x^2
\]
Next, combine the like terms \( -12x - 50x \):
\[
A = 600 - 62x + x^2
\]
Therefore, the expression that represents the area of the rectangle is:
\[
A = x^2 - 62x + 600
\]
Without the options \( A, B, C, D \) specifically, this is the expression you would be looking for! If you have specific answer choices, please provide them, and I can help identify the correct one.
First, let's simplify the expression for the length:
\[
\text{Length} = (2 - x) + 10 = 12 - x
\]
Now, we have:
- Length: \( 12 - x \)
- Width: \( 50 - x \)
Next, we can calculate the area \( A \) of the rectangle:
\[
A = \text{Length} \times \text{Width} = (12 - x)(50 - x)
\]
Now, we can expand this expression using the distributive property (also known as the FOIL method for binomials):
\[
A = (12)(50) + (12)(-x) + (-x)(50) + (-x)(-x)
\]
Calculating each term:
1. \( 12 \times 50 = 600 \)
2. \( 12 \times -x = -12x \)
3. \( -x \times 50 = -50x \)
4. \( -x \times -x = x^2 \)
Combining these results, we get:
\[
A = 600 - 12x - 50x + x^2
\]
Next, combine the like terms \( -12x - 50x \):
\[
A = 600 - 62x + x^2
\]
Therefore, the expression that represents the area of the rectangle is:
\[
A = x^2 - 62x + 600
\]
Without the options \( A, B, C, D \) specifically, this is the expression you would be looking for! If you have specific answer choices, please provide them, and I can help identify the correct one.