Question

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.

Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1.

Answer 1

Perimeter of rectangle2 = k × perimeter of rectangle 1

area of rectangle 2 = k² × area of rectangle 1

Explanation:

• rectangle 1 :

Length x

Width y

perimeter1 = 2×(x + y)

area1 = x × y

……………………

•• rectangle 2 :

Length kx

Width ky

Perimeter2 = 2×(Kx + ky)

area2 = kx × ky

……………………………………………

therefore,

Perimeter of rectangle 2

= 2×(Kx + ky)

= 2×k×(x + y)

= k×2×(x + y)

= k × perimeter of rectangle 1

On the other hand,

area of rectangle 2

= Kx × ky

= k×k×(x × y)

= k²×(x × y)

= k² × area of rectangle 1