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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
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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

 

 

 

 

cool cool cool

CPhill  Feb 9, 2018
edited by CPhill  Feb 9, 2018
 #2
avatar+190 
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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

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