Question
A rectangle is to be constructed with 60 meters of wire. The rectangle will have an area of \( A=30 x-x^{2} \), where \( x \) is the length of one side of the rectangle. Using the equation, state the area o the rectangle if one side is 9 meters
Ask by Page Mann. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The area of the rectangle when one side is 9 meters is 189 square meters.
Solution
To determine the area of the rectangle when one side is 9 meters, we'll use the given area equation:
\[
A = 30x - x^2
\]
Here, \( x \) represents the length of one side of the rectangle. Let's substitute \( x = 9 \) meters into the equation:
\[
A = 30(9) - (9)^2
\]
\[
A = 270 - 81
\]
\[
A = 189 \text{ square meters}
\]
**Therefore, the area of the rectangle when one side is 9 meters is **\( \boxed{189\ \text{m}^2} \)**.
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Simplify this solution Beyond the Answer
If one side of the rectangle is \( x = 9 \) meters, we can substitute this value into the area equation \( A = 30x - x^2 \). Plugging in the value, we get: \[ A = 30(9) - (9)^2 = 270 - 81 = 189 \text{ square meters.} \] So, the area of the rectangle when one side is 9 meters is 189 square meters. To ensure you’re maximizing your area effectively, double-check constraints! Given you have a perimeter of 60 meters, both dimensions must add up correctly. With a rectangle made of 60 meters of wire, the sum of all sides dictates that \( 2l + 2w = 60 \), which simplifies down to \( l + w = 30 \). Ensure your \( x \) fits within those dimensions to avoid surprise equations!
