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A rectangular swimming pool has a length twice as long as its width. The pool has a sidewalk around it that is 2 feet wide. Write an expression that would help you find the area of the pool and its sidewalk.

Respuesta :

kudzordzifrancis

Answer:

[tex]A=2 {w}^{2}+12w+16\: square\:feet[/tex]

Step-by-step explanation:

The width(W) of the pool

[tex] = w[/tex]

This implies that, the length (L) of the sw

imming pool is

[tex] = (2w)feet[/tex]

Also the width of the swimming pool with the sidewalk

[tex] = (w + 4)feet[/tex]

And the length of the swimming pool with the sidewalk

[tex] = (2w + 4)feet[/tex]

Area of the swimming pool is given by

[tex]A = Length\times Width[/tex]

Writing expression for the area of swimming pool together with the sidewalk, we obtained

[tex]A=(w+4)(2w+4) [/tex]

[tex]A=w(2w+4)+4(2w+4)[/tex]

[tex]A=2 {w}^{2} +4w+8w+16[/tex]

[tex]A=2 {w}^{2}+12w+16[/tex]

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