# UWorld SAT Question of the Week

Interpret a polynomial expression in the context of area and volume

The length of a rectangular youth football field is 5 less than 2 times the width. If the width of the field is *w* yards, which of the following could represent the area *A*(*w *), in square yards, of the field?

Hint: The formula for the area of a rectangle isA=lw, wherelis the length andwis the width.

The function notationA(w) means the area of the field in terms of the lengthw.

The formula for the area of a rectangle is *A*=*lw*, where *l* is the length and *w* is the width. It is given that the **length is 5 less than 2 times the width**, so *l* = 2*w *– 5

The function notation *A*(*w *) means the area in terms of the length *w*. Substitute 2*w* – 5 for *l* into the expression for area to **write an expression for A(w )**.

*A*(

*w*) = (2

*w*– 5)

*w*

Distribute *w* to each term in 2*w* − 5 to find the area of the field.

A(w ) = (2w − 5)w | |

A(w ) = 2w ^{2} − 5w | Distribute w to 2w − 5 |

The area of the field, in square yards, is ** A(w ) = 2w ^{2} − 5w**.

**(Choice A)** *A*(*w *) = 3*w* − 5 may result from mistakenly adding (instead of multiplying) the length and the width of the field.

**(Choice B)** *A*(*w *) = 2*w *^{2} may result from mistaking the length to be *2 times the width*, but it is given that the length is *5 less than 2 times the width*.

**(Choice D)** *A*(*w *) = 3*w *^{2} may result from the misconception that “5 less than 2 times the width” can be represented by (5 − 2)*w* instead of 2*w* − 5.

**Things to remember:**

The formula for the area of a rectangle is *A* =* lw* where *l * is the length and *w * is the width.

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