If each dimension of a rectangle decreases by 1, its area will decrease from 2017 to \(1917\). What will be the area of the rectangle if each of its dimensions increases by 1?
+1622 First label the dimensions of the rectangle, let the width of the rectangle be \(w\) and the length of the rectangle be \(l\).
Now to write some equations:
\(wl = 2017\)
\((w - 1)(l - 1) = 1917\)
Now we will foil equation 2.
\(wl - w - l + 1 = 1917 \)
Substitution:
\(2017 - w - l + 1 = 1917 \)
Now we can get:
\(w + l = 101\)
Since we are looking for \((w + 1)(l + 1)\)because we want the dimensions increased by 1, we can factor that binomial to get:
\(wl + w + l + 1\) which is what we are looking for.
Now we can substitute:
2017 + 101 + 1 = 2119 = Answer
