Question

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:

Answer 1

Answer:

Rectangle 1 : length = x ; width = y

Rectangle 2 : length = kx ; width = ky

Step-by-step explanation:

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

For my teacher, I John Boles solved it.

Answer 2

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