+0  
 
0
95
1
avatar

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?

 Jan 22, 2022
 #1
avatar+565 
-5

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

 

 

smiley

 Jan 23, 2022

19 Online Users