Podcast
Questions and Answers
The formula for the perimeter $P$ of a rectangle is given by $P = 2l + 2w$, where $l$ is the length and $w$ is the ______.
The formula for the perimeter $P$ of a rectangle is given by $P = 2l + 2w$, where $l$ is the length and $w$ is the ______.
width
Given a fixed perimeter, a ______ area is achieved when the rectangle approaches a square.
Given a fixed perimeter, a ______ area is achieved when the rectangle approaches a square.
maximum
If the total fencing available is 100 feet and the length is $l$ feet, the equation to find the width $w$ in terms of $l$ is $w = 50 - ______$.
If the total fencing available is 100 feet and the length is $l$ feet, the equation to find the width $w$ in terms of $l$ is $w = 50 - ______$.
l
The area $A$ of a rectangle garden with length $l$ and width $w$ is given by the formula $A = l \times ______$.
The area $A$ of a rectangle garden with length $l$ and width $w$ is given by the formula $A = l \times ______$.
With 100 feet of fencing, the area of the rectangular garden can be expressed as a function of length $l$. The equation is $A(l) = l(50-______)$.
With 100 feet of fencing, the area of the rectangular garden can be expressed as a function of length $l$. The equation is $A(l) = l(50-______)$.
If a rectangular garden has a length of 20 feet and a width of 30 feet, the total fencing required to enclose it is ______ feet.
If a rectangular garden has a length of 20 feet and a width of 30 feet, the total fencing required to enclose it is ______ feet.
The maximum area of a rectangular garden with a fixed perimeter of 100 feet occurs when the length and width are equal, making the garden a ______.
The maximum area of a rectangular garden with a fixed perimeter of 100 feet occurs when the length and width are equal, making the garden a ______.
If the length of a rectangular garden is 8 feet and the perimeter is 100 feet, the width of the garden is ______ feet.
If the length of a rectangular garden is 8 feet and the perimeter is 100 feet, the width of the garden is ______ feet.
If the length of the rectangular garden is represented by $l$, the width is represented by $50-l$, then the area can be expressed as $50l-______$.
If the length of the rectangular garden is represented by $l$, the width is represented by $50-l$, then the area can be expressed as $50l-______$.
Given that the area $A$ of a rectangular garden can be represented by the equation $A(l) = 50l - l^2$, the area when $l = 24$ feet is ______ square feet.
Given that the area $A$ of a rectangular garden can be represented by the equation $A(l) = 50l - l^2$, the area when $l = 24$ feet is ______ square feet.
Flashcards
Perimeter of a rectangle
Perimeter of a rectangle
The total length of the boundary of a rectangle.
Perimeter formula
Perimeter formula
For a rectangle: 2 * (length + width)
Fencing Constraint
Fencing Constraint
Surrounding the garden with 100 feet of fencing imposes a constraint that total perimeter is 100 feet.
Width equation w(l)
Width equation w(l)
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Area of a rectangle
Area of a rectangle
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Area equation a(l)
Area equation a(l)
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Using the formula a(l) = l * (50 - l)
Using the formula a(l) = l * (50 - l)
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Study Notes
- A garden has been eaten by rabbits, requiring fencing.
- 100 feet of fencing is available for the rectangular garden.
Garden Dimensions and Area
- The task is to find the unknown width and area for each given length.
- Length: 8 feet, Width: 42 feet, Area: 336 square feet
- Length: 16 feet, Width: 34 feet, Area: 544 square feet
- Length: 24 feet, Width: 26 feet, Area: 624 square feet
- Length: l feet, Width: 50-l feet, Area: l(50-l) square feet
Equations
- Equation for width w as a function of length l: w(l) = 50 - l
- Equation for area a as a function of length l: a(l) = 50l - l^2
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