Answer:
a) Similar
b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)
c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)
Step-by-step explanation:
Given:
Rectangle 1 has length = x
Rectangle 1 has width = y
Rectangle 2 has length = kx
Rectangle 2 has width = ky
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Perimeter of Rectangle = 2*(Length + Width)
Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y
Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky
= k(2x+2y)
= k(Perimeter of Rectangle 1)
Hence proved that 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 k^2 times the area of Rectangle 1.
Area of Rectangle = Length * width
Area of Rectangle 1 = x * y
Area of Rectangle 2 = kx*ky
= k^2 (xy)
= k^2 (Area of rectangle 1)
Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.
