1998 CEMC Gauss (Grade 7) Problems/Problem 11

Problem

Kalyn cut rectangle R from a sheet of paper. A smaller rectangle is then cut from the large rectangle R to produce figure S. In comparing R to S,

[R is a rectangle with sides 8 and 6 cm. S is the same as R with a 4x1 rectangle cut from one of its corners.]

$\text{(A) the area and perimeter both decrease}$

$\text{(B) the area decreases and the perimeter increases}$

$\text{(C) the area and perimeter both increase}$

$\text{(D) the area increases and the perimeter decreases}$

$\text{(E) the area decreases and the perimeter stays the same}$

Because a section of R is cut out to form S, the area of S is smaller than the area of R.

The perimeter of R is $2(6) + 2(8) = 28$ cm and the perimeter of S is $6 + 8 + 5 + 4 + 1 +4 = 28$ cm, so the perimeters of both shapes are equal.

The answer is $\boxed{\text{(E)}}.$

-edited by coolmath34