Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0.

(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?

(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

(c) Write a paragraph proof to show that the area of Rectangle 2 ismtimes the area of Rectangle 1.

(a) The Rectangles are similar because all angles of all rectangles are equal to 90°. Then, the corresponding sides have the equivalent ratio equal to k.

(b) The perimeter of the rectangle is the sum of the measurements of all sides. Such that for Rectangle 1, it should be.

Perimeter (Rectangle 1) = 2x + 2y

Then for rectangle 2,

Perimeter (Rectangle 2) = 2kx + 2ky = k (2x + 2y)

= k (Perimeter of rectangle 1)

c. Area of rectangle is the product of the lengths of two sides, (x) (y). For Rectangle 2, that would be (kx) (ky) = k²xy