1. 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.

I feel like this is a huge math word problem and wish I could go back to when the word problems were: If Sally had 5 apples and Johney ate 2 apples, how many apples does Sally have left?

lol Sorry

Thank You

KennedyPape
Feb 9, 2018

#1**+1 **

1. 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.

Not as bad as it looks

a) Note that the dimensions of Rectangle 2 are just 2x and 2y

They are similar because the ratio of their corresponding dimensions is the same

To prove this :

Length of Rec 2 = 2x Width of Rec 2 = 2y

_____________ __ = 2 ___________ __ = 2

Length of Rec 1 x Width of Rec 1 y

b) You can write your paragraphs based on these :

Perimeter of Rec 1 = 2(W + L ) = 2 (x + y)

Perimeter of Rec 2 = 2 (W + L ) = 2 (2x + 2y) = 2 (2 (x + y)) = 4(x + y) =

2 * [ 2(x + y) ] = 2 times the perimeter of Rec 1

c)

Area of Rec 1 = xy

Area of Rec 2 = 2x * 2y = 4 [xy] = 4 times the area of Rec 1

CPhill
Feb 9, 2018

#2**0 **

I was hoping you could go over my paragraph proofs for questions (b) and (c).

(b) The perimeter of the rectangle is the sum of the measurements of all sides. Rectangle 1 should be, 2(W+L)=2(x+y). Rectangle 2 should be, 2(W+L)=2(2x+2y)=2(2(x+y)=4(x+y)=2[2(x+y)]. Which then simplifies to 2 times the perimeter of Rectangle 1.

(c) The area of a rectangle is the product of the lengths of two sides. To find Rectangle 1’s area you would multiply (x)(y). For Rectangle 2 the area formula would be (kx)(ky)=k^2*xy. Which would make Rectangle 2 k^2 times the area of Rectangle 1.

My other paragraph proof for (b) was...But didn't know if it as correct.:

The perimeter of the rectangle is the sum of the measurements of all sides. Rectangle 1 should be, Perimeter(Recangle 1)=2x+2y. Rectangle 2 should be, Perimeter(Recangle 2)=2kx+2ky. Which then simplifies to 2 times the k(2x+2y)=k(Perimeter of Rectangle 1).

Sorry to bother you with this. Thank You!

KennedyPape
Feb 10, 2018