Question
An ecology center wants to set up an experimental garden. It has 180 meters of fencing to enclose a rectangular area of 2000 square meters. Find the length and width of the rectangle by completing parts (a) through (c) below. (a) Let \( \mathrm{x}= \) the length and write an expression for the width. \( 90-\mathrm{x} \) (Simplify your answer.) (b) Write an equation relating the length, width, and area, using the result of part (a). (Do not simplify.)
Ask by Rogers Bowman. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Equation:**
\[
x \times (90 - x) = 2000
\]
Solution
### Problem (b):
**Write an equation relating the length, width, and area, using the result of part (a).**
From part (a), we have:
\[
\text{Width} = 90 - x
\]
The area of the rectangle is given by:
\[
\text{Area} = \text{Length} \times \text{Width} = x \times (90 - x)
\]
Given that the area is 2000 square meters, we can set up the equation:
\[
x \times (90 - x) = 2000
\]
**Answer:**
\[
\mathrm{x} \times (90 - \mathrm{x}) = 2000
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To set up the experimental garden, you can use the fencing to create a rectangle. Given that the total fencing amounts to 180 meters, the equation for the perimeter can be expressed as \( 2x + 2y = 180 \). Simplifying that gives \( x + y = 90 \). Thus, the width, \( y \), can be directly expressed as \( y = 90 - x \). Using the area requirement of 2000 square meters, you can now relate the length and width in terms of \( x \). Plugging the expression for the width into the area formula \( A = x \cdot y \), we get \( 2000 = x(90 - x) \). This equation now relates the length \( x \), the width \( y \), and the area of your garden!
