Maximizing Garden Area Dimensions

Maximizing Garden Area Dimensions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial by Patrick explains how to solve a quadratic word problem involving a rectangular garden bounded by a house and enclosed by 100 meters of fencing. The goal is to find the dimensions that maximize the garden's area. The tutorial covers setting up the constraint equation, transforming the area equation, testing different values, and finding the vertex of the quadratic equation to determine the maximum area dimensions.

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18 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the total length of fencing available for the garden?

50 meters

75 meters

100 meters

150 meters

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which side of the garden is bounded by the house?

None of the sides

One of the sides

The shorter side

The longer side

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What shape is the garden?

Circular

Square

Triangular

Rectangular

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What variables are introduced to represent the dimensions of the garden?

m and n

a and b

x and y

p and q

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation derived from the fencing constraint?

x + 2y = 100

2x + 2y = 100

2x + y = 100

x + y = 100

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for the area of the garden in terms of x and y?

x^2 + y^2

2x + y

x * y

x + y

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the area function simplified to a quadratic function?

By substituting y in terms of x

By multiplying x and y

By adding x and y

By dividing x by y

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