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 is k2 times the area of rectangle 1.

a) yes they are similar

b)Proved below

c)Proved below

Step-by-step explanation:

a) rectangle 1 and 2 are similar by definition of similar rectangles.

Definition of similar rectangles states that two rectangles are similar if they have same shape but different sizes. The ratio between their corresponding sides are same, in this case as rectangle 2 is made by multiplying each dimension of Rectangle 1 by a

factor of k, where k>0 thus providing same proportion in length of different corresponding sides of two rectangles hence rectangle 1 and 2 are similar.

b) Perimeter of rectangle 1, P1= s1+ s2+ s3 + s4

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

  Perimeter of rectangle 2, P2= k.s1+ k.s2+ k.s3 + k.s4

Taking k common

                                                  = k(s1+ s2+ s3 + s4)

Substituting P1 in above expression

                                               P2  =k(P1)

Hence the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

c) Area of rectangle 1, A1= 2(s1)(s2)

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

Area of rectangle 2, A2= 2(k.s1)(k.s2)

                                       = 2k^2(s1)(s2)

                                        = k^2 [2(s1)(s2)]

Substituting A1 in above expression

                                        A2 = k^2(A1)

Hence the area of Rectangle 2 is k2 times the area of Rectangle 1 !

search the worksheet up on the internet

step-by-step explanation:

it works trust me