The smith family is designing new plans for an in ground pool. mr smith draws a rectangular shape with a length that is 5 feet longer than the height. write a polynomial expression that represent the area of the pool.

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The smith family is designing new plans for an in ground pool. mr smith draws a rectangular shape with a length that is 5 feet longer than the height. write a polynomial expression that represent the area of the pool.

area = w(w+5) = w^2 + 5w square units

Explanation:

The pool has a rectangular shape. Area of rectangle can be calculated by multiplying its length and width.

We are given that:

length = w + 5

width = w

Therefore:

Area of pool = length * width

= (w+5) * w

= w(w+5) = w^2 + 5w square units

Hope this helps 🙂

Answer

Are of the pool = w² + 5w (in square feet)

Explanation

Since the pool is rectangular in shape,

Area of the pool can be calculated using the formula for the area of a rectangle

Area of rectangle = length x width

Given,

Width of pool (Assume is same as height) = w

Length of pool= w + 5

Area = w * (w + 5)

= w² + 5w (in square feet)

where w is the width of the pool

area of pool = w(w+5) = w^2 + 5w square feet

Explanation:

The height of the pool is used as its width.

Assume that the width of the pool is w feet.

Now, we are given that the length of the pool is 5 feet longer than its width.

This means that:

length of the pool = w + 5 feet

The area of the rectangle is calculated as follows:

area = length * width

area = (w+5) * (w)

area = w^2 + 5w square feet

Hope this helps 🙂

total area = w^2 + 13w + 36 ft^2

Explanation:

The final pool and the sideways will be as shown in the attachment

1- We will get the area of the pool:

length of pool = w + 5

width of pool = w

area of pool = length * width

area of pool = w (w+5) square ft ...........> I

2- We will get the area of the sideways:

The side way is composed of the two blue rectangles and the two green ones

Therefore:

area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)

a- getting the area of the blue rectangle:

length = w + 5 + 2 + 2 = w+9

width = 2

area of blue rectangle = length * width

area of blue rectangle = 2(w+9) square ft ..........> a

b- getting the area of the green rectangle:

length = w

width = 2

area of green rectangle = length * width

area of green rectangle = 2w square ft ..............> b

c- getting area of sideways:

as mentioned before:

area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)

area of sideways = 2*equation a + 2*equation b

area of sideways = 2 (2(w+9)) + 2(2w)

area of sideways = 4(w+9) + 4w

area of sideways = 4w + 36 + 4w

area of sideways = 8w + 36 ...........> II

3- getting the total area:

total area = area of pool + area of sideways

total area = equation I + equation II

total area = w (w+5) + 8w + 36

total area = w^2 + 5w + 8w + 36

total area = w^2 + 13w + 36 ft^2

Hope this helps 🙂

[tex]Asap the smith family is designing new plans for an in-ground pool. mr. smith draws a rectangular s[/tex]

To solve this problem you must apply the proccedure shown below:

1- The formula for calculate the area of this rectangle is:

[tex]A=LH[/tex]

Where [tex]L[/tex] is the length and [tex]H[/tex] is the heigth.

2. Let's call identify the heigth with the variable [tex]x[/tex].

3. If the length is [tex]5ft[/tex] longer than the heigth, you have:

[tex]L=x+5[/tex]

4. Therefore, you can write the following polynomial expression:

[tex]A(x)=x(x+5)\\ A(x)=x^{2} +5x[/tex]

5. If you know the value of the heigth, you can susbstitute it into the polynomial expression shown above and you will obtain the area.

Therefore, the answer is: [tex]A(x)=x^{2} +5x[/tex]

total area = w^2 + 13w + 36 ft^2

Explanation:

The final pool and the sideways will be as shown in the attachment

1- We will get the area of the pool:

length of pool = w + 5

width of pool = w

area of pool = length * width

area of pool = w (w+5) square ft ...........> I

2- We will get the area of the sideways:

The side way is composed of the two blue rectangles and the two green ones

Therefore:

area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)

a- getting the area of the blue rectangle:

length = w + 5 + 2 + 2 = w+9

width = 2

area of blue rectangle = length * width

area of blue rectangle = 2(w+9) square ft ..........> a

b- getting the area of the green rectangle:

length = w

width = 2

area of green rectangle = length * width

area of green rectangle = 2w square ft ..............> b

c- getting area of sideways:

as mentioned before:

area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)

area of sideways = 2*equation a + 2*equation b

area of sideways = 2 (2(w+9)) + 2(2w)

area of sideways = 4(w+9) + 4w

area of sideways = 4w + 36 + 4w

area of sideways = 8w + 36 ...........> II

3- getting the total area:

total area = area of pool + area of sideways

total area = equation I + equation II

total area = w (w+5) + 8w + 36

total area = w^2 + 5w + 8w + 36

total area = w^2 + 13w + 36 ft^2

Hope this helps 🙂

[tex]The smith family is designing new plans for an in-ground pool. mr. smith draws a rectangular shape w[/tex]

Area of rectangle is length times width

A = (w+5)×w = w^2 + 5w