QuestionAn ecology center has 260 m of fencing for a rectangular garden of 4000 m². Find length and width.
(a) Let $\mathrm{x}=$ length; width is $130-x$ .
(b) Write an equation for length, width, and area.

Studdy Solution

STEP 1

Assumptions1. The total length of fencing is260 meters. . The area of the rectangular garden is4000 square meters.
3. The shape of the garden is a rectangle.
4. Let x be the length of the rectangle.

STEP 2

First, we need to understand that the total length of fencing is the perimeter of the rectangle. The formula for the perimeter of a rectangle is2(length + width).
$Perimeter =2(length + width)$

STEP 3

We know that the total length of fencing is260 meters, so we can set up the equation $260 =2(length + width)$

STEP 4

We know that the length of the rectangle is x, so we can substitute x into the equation $260 =2(x + width)$

STEP 5

olving this equation for width, we get $width =130 - x$ This is the answer to part (a).

STEP 6

Next, we need to write an equation relating the length, width, and area of the rectangle. The formula for the area of a rectangle is length times width.
$Area = length \\times width$

STEP 7

We know that the area of the rectangle is4000 square meters, and we have an expression for the width from part (a). So we can substitute these values into the equation $4000 = x \\times (130 - x)$ This is the answer to part (b).

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QuestionAn ecology center has 260 m of fencing for a rectangular garden of 4000 m². Find length and width.
(a) Let $\mathrm{x}=$ length; width is $130-x$ .
(b) Write an equation for length, width, and area.

Studdy Solution

STEP 1

Assumptions1. The total length of fencing is260 meters. . The area of the rectangular garden is4000 square meters.
3. The shape of the garden is a rectangle.
4. Let x be the length of the rectangle.

STEP 2

First, we need to understand that the total length of fencing is the perimeter of the rectangle. The formula for the perimeter of a rectangle is2(length + width).
$Perimeter =2(length + width)$

STEP 3

We know that the total length of fencing is260 meters, so we can set up the equation $260 =2(length + width)$

STEP 4

We know that the length of the rectangle is x, so we can substitute x into the equation $260 =2(x + width)$

STEP 5

olving this equation for width, we get $width =130 - x$ This is the answer to part (a).

STEP 6

Next, we need to write an equation relating the length, width, and area of the rectangle. The formula for the area of a rectangle is length times width.
$Area = length \\times width$

STEP 7

We know that the area of the rectangle is4000 square meters, and we have an expression for the width from part (a). So we can substitute these values into the equation $4000 = x \\times (130 - x)$ This is the answer to part (b).

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QuestionAn ecology center has 260 m of fencing for a rectangular garden of 4000 m². Find length and width. (a) Let x=\mathrm{x}=x= length; width is 130−x130-x130−x. (b) Write an equation for length, width, and area.

Studdy Solution

STEP 1

Assumptions1. The total length of fencing is260 meters. . The area of the rectangular garden is4000 square meters.3. The shape of the garden is a rectangle.4. Let x be the length of the rectangle.

STEP 2

First, we need to understand that the total length of fencing is the perimeter of the rectangle. The formula for the perimeter of a rectangle is2(length + width).Perimeter=2(length+width)Perimeter =2(length + width)Perimeter=2(length+width)

STEP 3

We know that the total length of fencing is260 meters, so we can set up the equation260=2(length+width)260 =2(length + width)260=2(length+width)

STEP 4

We know that the length of the rectangle is x, so we can substitute x into the equation260=2(x+width)260 =2(x + width)260=2(x+width)

STEP 5

olving this equation for width, we getwidth=130−xwidth =130 - xwidth=130−xThis is the answer to part (a).

STEP 6

Next, we need to write an equation relating the length, width, and area of the rectangle. The formula for the area of a rectangle is length times width.Area=lengthtimeswidthArea = length \\times widthArea=lengthtimeswidth

STEP 7

We know that the area of the rectangle is4000 square meters, and we have an expression for the width from part (a). So we can substitute these values into the equation4000=xtimes(130−x)4000 = x \\times (130 - x)4000=xtimes(130−x)This is the answer to part (b).

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionAn ecology center has 260 m of fencing for a rectangular garden of 4000 m². Find length and width.
(a) Let $\mathrm{x}=$ length; width is $130-x$ .
(b) Write an equation for length, width, and area.

Assumptions1. The total length of fencing is260 meters. . The area of the rectangular garden is4000 square meters.
3. The shape of the garden is a rectangle.
4. Let x be the length of the rectangle.

First, we need to understand that the total length of fencing is the perimeter of the rectangle. The formula for the perimeter of a rectangle is2(length + width).
$Perimeter =2(length + width)$

We know that the total length of fencing is260 meters, so we can set up the equation $260 =2(length + width)$

We know that the length of the rectangle is x, so we can substitute x into the equation $260 =2(x + width)$

olving this equation for width, we get $width =130 - x$ This is the answer to part (a).

Next, we need to write an equation relating the length, width, and area of the rectangle. The formula for the area of a rectangle is length times width.
$Area = length \\times width$

We know that the area of the rectangle is4000 square meters, and we have an expression for the width from part (a). So we can substitute these values into the equation $4000 = x \\times (130 - x)$ This is the answer to part (b).