QuestionFind the length and width of a rectangular court where length is $9$ ft longer than twice the width and perimeter is $108$ ft.

Studdy Solution

STEP 1

Assumptions1. The length of the rectangular court is9 ft longer than twice the width. . The perimeter of the court is108 ft.
3. We need to find the length and width of the court.

STEP 2

Let's denote the width of the rectangular court as $w$ (in feet). Then, according to the problem, the length of the court is $2w +9$ (in feet).

STEP 3

The formula for the perimeter of a rectangle is given by $=2l +2w$ , where $l$ is the length and $w$ is the width.

STEP 4

We can substitute the values of $l$ and $$ from the problem into the formula for the perimeter. This gives us the equation $108 =2(2w +9) +2w$.

STEP 5

implify the equation.
$108 =4w +18 +2w$

STEP 6

Combine like terms.
$108 =6w +18$

STEP 7

Subtract18 from both sides of the equation to isolate the term with $w$ .
$108 -18 =6w$

STEP 8

implify the left side of the equation.
$90 =6w$

STEP 9

Divide both sides of the equation by6 to solve for $w$ .
$w =90 /6$

STEP 10

Calculate the value of $w$ .
$w =15$

STEP 11

Now that we have the width of the court, we can find the length by substituting $w$ into the equation $l =w +9$ .
$l =(15) +9$

STEP 12

Calculate the value of $l$ .
$l =30 +9 =39$ The length of the court is39 ft and the width is15 ft.

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QuestionFind the length and width of a rectangular court where length is $9$ ft longer than twice the width and perimeter is $108$ ft.

Studdy Solution

STEP 1

Assumptions1. The length of the rectangular court is9 ft longer than twice the width. . The perimeter of the court is108 ft.
3. We need to find the length and width of the court.

STEP 2

Let's denote the width of the rectangular court as $w$ (in feet). Then, according to the problem, the length of the court is $2w +9$ (in feet).

STEP 3

The formula for the perimeter of a rectangle is given by $=2l +2w$ , where $l$ is the length and $w$ is the width.

STEP 4

We can substitute the values of $l$ and $$ from the problem into the formula for the perimeter. This gives us the equation $108 =2(2w +9) +2w$.

STEP 5

implify the equation.
$108 =4w +18 +2w$

STEP 6

Combine like terms.
$108 =6w +18$

STEP 7

Subtract18 from both sides of the equation to isolate the term with $w$ .
$108 -18 =6w$

STEP 8

implify the left side of the equation.
$90 =6w$

STEP 9

Divide both sides of the equation by6 to solve for $w$ .
$w =90 /6$

STEP 10

Calculate the value of $w$ .
$w =15$

STEP 11

Now that we have the width of the court, we can find the length by substituting $w$ into the equation $l =w +9$ .
$l =(15) +9$

STEP 12

Calculate the value of $l$ .
$l =30 +9 =39$ The length of the court is39 ft and the width is15 ft.

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QuestionFind the length and width of a rectangular court where length is 999 ft longer than twice the width and perimeter is 108108108 ft.

Studdy Solution

STEP 1

Assumptions1. The length of the rectangular court is9 ft longer than twice the width. . The perimeter of the court is108 ft.3. We need to find the length and width of the court.

STEP 2

Let's denote the width of the rectangular court as www (in feet). Then, according to the problem, the length of the court is 2w+92w +92w+9 (in feet).

STEP 3

The formula for the perimeter of a rectangle is given by =2l+2w =2l +2w=2l+2w, where lll is the length and www is the width.

STEP 4

We can substitute the values of lll and $$ from the problem into the formula for the perimeter. This gives us the equation $108 =2(2w +9) +2w$.

STEP 5

implify the equation.108=4w+18+2w108 =4w +18 +2w108=4w+18+2w

STEP 6

Combine like terms.108=6w+18108 =6w +18108=6w+18

STEP 7

Subtract18 from both sides of the equation to isolate the term with www.108−18=6w108 -18 =6w108−18=6w

STEP 8

implify the left side of the equation.90=6w90 =6w90=6w

STEP 9

Divide both sides of the equation by6 to solve for www.w=90/6w =90 /6w=90/6

STEP 10

Calculate the value of www.w=15w =15w=15

STEP 11

Now that we have the width of the court, we can find the length by substituting www into the equation l=w+9l =w +9l=w+9.l=(15)+9l =(15) +9l=(15)+9

STEP 12

Calculate the value of lll.l=30+9=39l =30 +9 =39l=30+9=39The length of the court is39 ft and the width is15 ft.

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QuestionFind the length and width of a rectangular court where length is $9$ ft longer than twice the width and perimeter is $108$ ft.

Assumptions1. The length of the rectangular court is9 ft longer than twice the width. . The perimeter of the court is108 ft.
3. We need to find the length and width of the court.

Let's denote the width of the rectangular court as $w$ (in feet). Then, according to the problem, the length of the court is $2w +9$ (in feet).

The formula for the perimeter of a rectangle is given by $=2l +2w$ , where $l$ is the length and $w$ is the width.

We can substitute the values of $l$ and $$ from the problem into the formula for the perimeter. This gives us the equation $108 =2(2w +9) +2w$.

implify the equation.
$108 =4w +18 +2w$

Combine like terms.
$108 =6w +18$

Subtract18 from both sides of the equation to isolate the term with $w$ .
$108 -18 =6w$

implify the left side of the equation.
$90 =6w$

Divide both sides of the equation by6 to solve for $w$ .
$w =90 /6$

Calculate the value of $w$ .
$w =15$

Now that we have the width of the court, we can find the length by substituting $w$ into the equation $l =w +9$ .
$l =(15) +9$

Calculate the value of $l$ .
$l =30 +9 =39$ The length of the court is39 ft and the width is15 ft.