crackgmat007 wrote: ↑Sun Oct 11, 2009 12:40 pm
If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35. What is the perimeter of rectangle R?
24
37
48
50
51
Let L = the length of rectangle R
Let W = the width of rectangle R
If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72.
We can write: (L + 1)(W + 1) = 72
Expand to get:
LW + L + W + 1 = 72
If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35.
We can write: (L - 1)(W - 1) = 35
Expand to get:
LW - L - W + 1 = 35
What is the perimeter of rectangle R?
The perimeter = L + W + L + W =
2L + 2W
So far we have:
LW + L + W + 1 = 72
LW - L - W + 1 = 35
When we subtract the bottom equation from the top equation we get:
2L + 2W = 37
Since the perimeter =
2L + 2W, we can see that the correct answer is B
