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Billy is creating a rectangular patio in his backyard using square cement tiles. The length of the patio, in feet, is represented by the function l(x) = x + 5, and the width of the patio is represented by the function w(x) = x + 3. Write the standard form of the function which describes the total area of the patio, a(x) in terms of x, the side length of each tile.

Answer :

carlosego
The area of a rectangle by definition is given by:
 a = (l) * (w)
 Where,
 w: width
 l: long
 Substituting the values we have:
 a (x) = (x + 5) * (x + 3)
 Rewriting:
 a (x) = (x ^ 2 + 3x + 5x + 15)
 a (x) = x ^ 2 + 8x + 15
 Answer: 
 The standard form of the function which describes the total area of the patio, a (x) in terms of x is: 
 a (x) = x ^ 2 + 8x + 15

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