Question
A hole is punched in a pice of metal to make a part for a machine. The sides of the hole are measured as x-2, while the sides of the metal part is x+7. What is the area of the metal part?
Answers
Answered by
GPT-4o mini
To find the area of the metal part, we need to determine the dimensions of the metal part itself, which are given as \( x + 7 \) for each side.
The area of a rectangle (or a part with rectangular dimensions) can be calculated using the formula:
\[
\text{Area} = \text{length} \times \text{width}
\]
If we assume that the dimensions \( x + 7 \) represent both the length and the width (i.e., it's a square metal part), then the area is calculated as follows:
\[
\text{Area} = (x + 7) \times (x + 7) = (x + 7)^2
\]
To expand this expression:
\[
\text{Area} = (x + 7)(x + 7) = x^2 + 14x + 49
\]
Therefore, the area of the metal part is:
\[
\text{Area} = x^2 + 14x + 49
\]
If you have specific numerical values for \( x \), you can substitute them into this quadratic expression to find the exact area. If not, the area in terms of \( x \) is \( x^2 + 14x + 49 \).
The area of a rectangle (or a part with rectangular dimensions) can be calculated using the formula:
\[
\text{Area} = \text{length} \times \text{width}
\]
If we assume that the dimensions \( x + 7 \) represent both the length and the width (i.e., it's a square metal part), then the area is calculated as follows:
\[
\text{Area} = (x + 7) \times (x + 7) = (x + 7)^2
\]
To expand this expression:
\[
\text{Area} = (x + 7)(x + 7) = x^2 + 14x + 49
\]
Therefore, the area of the metal part is:
\[
\text{Area} = x^2 + 14x + 49
\]
If you have specific numerical values for \( x \), you can substitute them into this quadratic expression to find the exact area. If not, the area in terms of \( x \) is \( x^2 + 14x + 49 \).