Answer:
a) yes they are similar
b)Proved below
c)Proved below
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 !