7 Questions
If the width of the new flowerbed is $x$ meters, what is the algebraic expression for the length of the flowerbed?
$x + 2$
Which algebraic expression represents the area of the new flowerbed in terms of $x$?
$x(x + 2)$
What is the polynomial expression for the total cost of the border installation at Rs 80 per meter, given the width of the flowerbed is $x$ meters?
$160x + 320$
What is the expression for the perimeter of the new flowerbed?
$4x + 4$
Which equation represents the total cost of the renovation if the budget is Rs 2000?
$160x + 320 = 2000$
If the total budget for the renovation is Rs 2000, what is the polynomial equation to determine the width $x$ that maximizes the area?
$160x + 320 = 2000$
What is the maximum area of the flowerbed that can be achieved within the budget constraints?
180 square meters
Study Notes
Case Scenario: Renovating a Rectangular Flowerbed
- A local gardening club is planning to renovate a rectangular flowerbed in the community park.
Question 1: Designing the Flowerbed
- The new flowerbed's length is 2 meters longer than its width, denoted as x meters.
- Algebraic expression for the length of the flowerbed: x + 2.
- Expression for the area of the flowerbed: (x + 2) × x or x^2 + 2x.
Question 2: Calculating Border Cost
- The cost of the border is Rs 80 per meter.
- The perimeter of the flowerbed is 2(x + 2) + 2x or 4x + 4.
- Polynomial expression for the total cost of the border installation: 80(4x + 4) or 320x + 320.
Question 3: Optimizing Dimensions
- The total budget allocated for the flowerbed renovation is Rs 2000.
- Equation for the total cost of the renovation: 320x + 320 + (x^2 + 2x).
- The width of the flowerbed that maximizes the area while staying within the budget needs to be determined.
- The maximum area of the flowerbed achievable within the budget constraints needs to be calculated.
A mathematical problem about designing a new flowerbed and calculating the cost of a border around it. The length of the new flowerbed is 2 meters longer than its width.
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