Question

Can someone please help me with this problem? I can't figure it out
The length of a rectangle is 3 less than twice the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by 2..

Answer 1

in general, the area of a rectangle is length*width (or L*W for short)

so "length of a rectangle is 3 less than twice the width" implies L = 2W - 3

making the current area = W(2W-3)

from there, if the length is increased by 5, and the width is decreased by 2, take the current length (2W-3) and add 5 to that inside the parentheses, then add 2 to the W (make sure to write it as (W+2) with parentheses on the outside. expand the expression w/ FOIL, compare it to the original to see how the area changes.

Answer 2

so it would be (w+2)(w-2)(l+5)(l-5)?

Answer 3

two things

1. keep the expression in terms of W only. it's easier to compare the before vs. after expressions if they're only in one variable

2. the width decreases by 2, so it's only (W-2), there's no (W+2) term anywhere. same logic with the length term, the length (which in terms of L, is 2W - 3) only increases by 5, so the new length is (2W - 3 + 5), there's no - 5 term anywhere.

Answer 4

so you solve for W then find out whats three times less than W?

Answer 5

You’re not solving for W (you can’t solve for W. We don’t know the exact area)

The area of the original rectangle is W(2W-3) where W is the width and (2W-3) is the length

After the length is increased by 5 and the width is decreased by 2, the new area expression is therefore (W-2)(2W-3 + 5)

Use FOIL to expand both area expressions then compare the areas before and after

Answer 6

2w^2-2w-4. this one is bigger