QuestionFind the width and length of a rectangular area fenced along a river, where length is 7 ft more than width and total fencing is 91 ft.

Studdy Solution

STEP 1

Assumptions1. The length of the fenced-in area is7 feet greater than the width. . The total amount of fencing to be used is91 feet.
3. The fenced-in area is a rectangle.
4. The river bank is one of the sides of the rectangle, so it does not need to be fenced.

STEP 2

Let's denote the width of the rectangle as $w$ and the length as $l$ . According to the problem, the length is7 feet greater than the width, so we can express the length as $l = w +7$ .

STEP 3

The total amount of fencing to be used is equal to the perimeter of the rectangle. However, since one side (the river bank) does not need to be fenced, the total amount of fencing will be equal to the sum of the lengths of the other three sides. This can be expressed as $2w + l =91$ .

STEP 4

Now we have a system of two equations1. $l = w +7$
2. $2w + l =91$

STEP 5

Substitute the expression for $l$ from the first equation into the second equation $2w + (w +7) =91$

STEP 6

implify the equation $3w + =91$

STEP 7

Subtract7 from both sides of the equation to isolate $3w$ $3w =91 -7$

STEP 8

Calculate the right side of the equation $3w =84$

STEP 9

Divide both sides of the equation by3 to solve for $w$ $w =84 /3$

STEP 10

Calculate the value of $w$ $w =28$

STEP 11

Now that we have the width, we can find the length by substituting $w =28$ into the first equation $l = w +7$

STEP 12

Substitute $w =28$ into the equation $l =28 +7$

STEP 13

Calculate the value of $l$ $l =35$ The width of the fenced-in area is28 feet and the length is35 feet.

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QuestionFind the width and length of a rectangular area fenced along a river, where length is 7 ft more than width and total fencing is 91 ft.

Studdy Solution

STEP 1

Assumptions1. The length of the fenced-in area is7 feet greater than the width. . The total amount of fencing to be used is91 feet.
3. The fenced-in area is a rectangle.
4. The river bank is one of the sides of the rectangle, so it does not need to be fenced.

STEP 2

Let's denote the width of the rectangle as $w$ and the length as $l$ . According to the problem, the length is7 feet greater than the width, so we can express the length as $l = w +7$ .

STEP 3

The total amount of fencing to be used is equal to the perimeter of the rectangle. However, since one side (the river bank) does not need to be fenced, the total amount of fencing will be equal to the sum of the lengths of the other three sides. This can be expressed as $2w + l =91$ .

STEP 4

Now we have a system of two equations1. $l = w +7$
2. $2w + l =91$

STEP 5

Substitute the expression for $l$ from the first equation into the second equation $2w + (w +7) =91$

STEP 6

implify the equation $3w + =91$

STEP 7

Subtract7 from both sides of the equation to isolate $3w$ $3w =91 -7$

STEP 8

Calculate the right side of the equation $3w =84$

STEP 9

Divide both sides of the equation by3 to solve for $w$ $w =84 /3$

STEP 10

Calculate the value of $w$ $w =28$

STEP 11

Now that we have the width, we can find the length by substituting $w =28$ into the first equation $l = w +7$

STEP 12

Substitute $w =28$ into the equation $l =28 +7$

STEP 13

Calculate the value of $l$ $l =35$ The width of the fenced-in area is28 feet and the length is35 feet.

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QuestionFind the width and length of a rectangular area fenced along a river, where length is 7 ft more than width and total fencing is 91 ft.

Studdy Solution

STEP 1

Assumptions1. The length of the fenced-in area is7 feet greater than the width. . The total amount of fencing to be used is91 feet.3. The fenced-in area is a rectangle.4. The river bank is one of the sides of the rectangle, so it does not need to be fenced.

STEP 2

Let's denote the width of the rectangle as www and the length as lll. According to the problem, the length is7 feet greater than the width, so we can express the length as l=w+7l = w +7l=w+7.

STEP 3

The total amount of fencing to be used is equal to the perimeter of the rectangle. However, since one side (the river bank) does not need to be fenced, the total amount of fencing will be equal to the sum of the lengths of the other three sides. This can be expressed as 2w+l=912w + l =912w+l=91.

STEP 4

Now we have a system of two equations1. l=w+7l = w +7l=w+72. 2w+l=912w + l =912w+l=91

STEP 5

Substitute the expression for lll from the first equation into the second equation2w+(w+7)=912w + (w +7) =912w+(w+7)=91

STEP 6

implify the equation3w+=913w + =913w+=91

STEP 7

Subtract7 from both sides of the equation to isolate 3w3w3w3w=91−73w =91 -73w=91−7

STEP 8

Calculate the right side of the equation3w=843w =843w=84

STEP 9

Divide both sides of the equation by3 to solve for wwww=84/3w =84 /3w=84/3

STEP 10

Calculate the value of wwww=28w =28w=28

STEP 11

Now that we have the width, we can find the length by substituting w=28w =28w=28 into the first equationl=w+7l = w +7l=w+7

STEP 12

Substitute w=28w =28w=28 into the equationl=28+7l =28 +7l=28+7

STEP 13

Calculate the value of llll=35l =35l=35The width of the fenced-in area is28 feet and the length is35 feet.

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Assumptions1. The length of the fenced-in area is7 feet greater than the width. . The total amount of fencing to be used is91 feet.
3. The fenced-in area is a rectangle.
4. The river bank is one of the sides of the rectangle, so it does not need to be fenced.

Let's denote the width of the rectangle as $w$ and the length as $l$ . According to the problem, the length is7 feet greater than the width, so we can express the length as $l = w +7$ .

The total amount of fencing to be used is equal to the perimeter of the rectangle. However, since one side (the river bank) does not need to be fenced, the total amount of fencing will be equal to the sum of the lengths of the other three sides. This can be expressed as $2w + l =91$ .

Now we have a system of two equations1. $l = w +7$
2. $2w + l =91$

Substitute the expression for $l$ from the first equation into the second equation $2w + (w +7) =91$

implify the equation $3w + =91$

Subtract7 from both sides of the equation to isolate $3w$ $3w =91 -7$

Calculate the right side of the equation $3w =84$

Divide both sides of the equation by3 to solve for $w$ $w =84 /3$

Calculate the value of $w$ $w =28$

Now that we have the width, we can find the length by substituting $w =28$ into the first equation $l = w +7$

Substitute $w =28$ into the equation $l =28 +7$

Calculate the value of $l$ $l =35$ The width of the fenced-in area is28 feet and the length is35 feet.