2. 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?

Yes, they are similar because rectangle 2 is a larger version of rectangle 1.

(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 is times the area of Rectangle 1.

Answer:

Rectangle 1 : length = x; width = y

Rectangle 2 : length = kx; width = ky

Let us assume that x = 10; y = 5; k = 2

Area:

Rectangle 1 : 10 x 5 = 50

Rectangle 2 : 10 (2) x 5 (2) = 20 x 10 = 200

a) Yes, these triangle are similar. Because Rectangle 2 is the enlarged version of Rectangle 1.

b) Perimeter:

Rectangle 1 = 2x + 2y

Rectangle 2 = 2kx + 2ky

Rectangle 2 is k times the perimeter of Rectangle 1

Rectangle 2 = k (Rectangle 1)

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

2kx + 2ky = 2kx + 2ky

c) Area:

Rectangle 1 = x * y

Rectangle 2 = kx * ky