carcass wrote:
The perimeter of rectangle A is 200 meters. The length of rectangle B is 10 meters less than the length of rectangle A and the width of rectangle B is 10 meters more than the width of rectangle A. If rectangle B is a square, what is the width, in meters, of rectangle A ?
A. 10
B. 20
C. 40
D. 50
E. 60
For the square (rectangle B) the net change in perimeter, from decreased L (-10), twice, and (+10) in W, twice, is 0.
All sides of a square are equal. If we add 10 to two sides, and subtract 10 from two sides,
because we started with equal side lengths, the perimeter does not change.
If rectangle-square B has side = 50.
Perimeter is 4s = 200.
Each L increases by 10 (to make rectangle A): two lengths = 60
Each W decreases by 10 (to make rectangle A): two widths = 40
Perimeter of rectangle A? 60 + 60 + 40 + 40 = 200 (same as rectangle-square B)
So the perimeter of rectangle A equals perimeter of square (rectangle B).
Perimeter of square = 4s
4s = 200
s = 50
If the side of the square (B) is 50, then the width of rectangle A is (50 - 10) = 40.
Answer C
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