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Class 9 Math: Renovating a Rectangular Flowerbed

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Class 9 Math: Renovating a Rectangular Flowerbed

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Questions and Answers

If the width of the new flowerbed is $x$ meters, what is the algebraic expression for the length of the flowerbed?

$x + 2$ (correct)

$x - 2$

$2x$

$2x + 1$

Which algebraic expression represents the area of the new flowerbed in terms of $x$?

$x^2 - 2$

$x^2 + 3x$

$x(x + 2)$ (correct)

$x^2 + 2$

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?

$160(x + 2)$

$320x + 160$

$320(x + 2)$

$160x + 320$ (correct)

What is the expression for the perimeter of the new flowerbed?

$4x + 4$ Signup and view all the answers

Which equation represents the total cost of the renovation if the budget is Rs 2000?

$160x + 320 = 2000$ Signup and view all the answers

If the total budget for the renovation is Rs 2000, what is the polynomial equation to determine the width $x$ that maximizes the area?

$160x + 320 = 2000$ Signup and view all the answers

What is the maximum area of the flowerbed that can be achieved within the budget constraints?

180 square meters Signup and view all the answers

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.

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Description

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.