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 k^2 times the area of Rectangle 1.
Accepted Solution
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Answer:a) Similarb) 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 = xRectangle 1 has width = yRectangle 2 has length = kxRectangle 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+2yPerimeter 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 * widthArea of Rectangle 1 = x * yArea 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.