Solved on Feb 09, 2024

Find the length of a pool with width 6 feet and perimeter $P=30$ feet using the formula $P=2L+2W$ .

STEP 1

Assumptions
1. The width of the pool (W) is 6 feet.
2. The total perimeter of the pool (P) is 30 feet.
3. The formula for the perimeter of a rectangle is $P = 2L + 2W$ , where L is the length and W is the width.

STEP 2

We need to find the length of the pool (L). To do this, we can rearrange the formula for the perimeter to solve for L.
$L = \frac{P - 2W}{2}$

STEP 3

Now, plug in the given values for the perimeter (P) and the width (W) to calculate the length (L).
$L = \frac{30 - 2 \times 6}{2}$

STEP 4

First, calculate the value inside the parentheses.
$L = \frac{30 - 12}{2}$

STEP 5

Subtract the numbers to find the value in the numerator.
$L = \frac{18}{2}$

STEP 6

Finally, divide the numerator by the denominator to find the length of the pool.
$L = \frac{18}{2} = 9$
The length of the pool is 9 feet, which corresponds to option b. $\mathrm{L}=9$ .

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Find the length of a pool with width 6 feet and perimeter $P=30$ feet using the formula $P=2L+2W$ .

STEP 1

Assumptions
1. The width of the pool (W) is 6 feet.
2. The total perimeter of the pool (P) is 30 feet.
3. The formula for the perimeter of a rectangle is $P = 2L + 2W$ , where L is the length and W is the width.

STEP 2

We need to find the length of the pool (L). To do this, we can rearrange the formula for the perimeter to solve for L.
$L = \frac{P - 2W}{2}$

STEP 3

Now, plug in the given values for the perimeter (P) and the width (W) to calculate the length (L).
$L = \frac{30 - 2 \times 6}{2}$

STEP 4

First, calculate the value inside the parentheses.
$L = \frac{30 - 12}{2}$

STEP 5

Subtract the numbers to find the value in the numerator.
$L = \frac{18}{2}$

STEP 6

Finally, divide the numerator by the denominator to find the length of the pool.
$L = \frac{18}{2} = 9$
The length of the pool is 9 feet, which corresponds to option b. $\mathrm{L}=9$ .

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Find the length of a pool with width 6 feet and perimeter P=30P=30P=30 feet using the formula P=2L+2WP=2L+2WP=2L+2W.

STEP 1

Assumptions1. The width of the pool (W) is 6 feet.2. The total perimeter of the pool (P) is 30 feet.3. The formula for the perimeter of a rectangle is P=2L+2W P = 2L + 2W P=2L+2W, where L is the length and W is the width.

STEP 2

We need to find the length of the pool (L). To do this, we can rearrange the formula for the perimeter to solve for L.L=P−2W2 L = \frac{P - 2W}{2} L=2P−2W​

STEP 3

Now, plug in the given values for the perimeter (P) and the width (W) to calculate the length (L).L=30−2×62 L = \frac{30 - 2 \times 6}{2} L=230−2×6​

STEP 4

First, calculate the value inside the parentheses.L=30−122 L = \frac{30 - 12}{2} L=230−12​

STEP 5

Subtract the numbers to find the value in the numerator.L=182 L = \frac{18}{2} L=218​

STEP 6

Finally, divide the numerator by the denominator to find the length of the pool.L=182=9 L = \frac{18}{2} = 9 L=218​=9The length of the pool is 9 feet, which corresponds to option b. L=9\mathrm{L}=9L=9.

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

Find the length of a pool with width 6 feet and perimeter $P=30$ feet using the formula $P=2L+2W$ .

Assumptions
1. The width of the pool (W) is 6 feet.
2. The total perimeter of the pool (P) is 30 feet.
3. The formula for the perimeter of a rectangle is $P = 2L + 2W$ , where L is the length and W is the width.

We need to find the length of the pool (L). To do this, we can rearrange the formula for the perimeter to solve for L.
$L = \frac{P - 2W}{2}$

Now, plug in the given values for the perimeter (P) and the width (W) to calculate the length (L).
$L = \frac{30 - 2 \times 6}{2}$

First, calculate the value inside the parentheses.
$L = \frac{30 - 12}{2}$

Subtract the numbers to find the value in the numerator.
$L = \frac{18}{2}$

Finally, divide the numerator by the denominator to find the length of the pool.
$L = \frac{18}{2} = 9$
The length of the pool is 9 feet, which corresponds to option b. $\mathrm{L}=9$ .