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.

Question

Mathematics

Double Bubble

26 September, 14:50

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.

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Brent · Answer 1

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