+0  
 
+1
323
3
avatar+238 

Original Question:

 

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.

 

 

Answers for (b) and (c):

 

(b): 

(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).

 

Thank You!

KennedyPape  Feb 10, 2018
 #1
avatar+7339 
+2

On your first paragraph proof for  (b) , you said, "Rectangle 2 should be, 2(W+L)=2(2x+2y)"

....Where did you get that the width and length of Rectangle 2 are  2x  and  2y   ?

 

Rectangle 1 has length x and width y .

 

Rectangle 2 has a length  kx  and a width  ky .

 

Perimeter of Rectangle 1   =   x + x + y + y

 

Perimeter of Rectangle 2   =   kx + kx + ky + ky   =   k(x + x + y + y)   =   k( Perimeter of Rectangle 1 )

 

Your second paragraph proof for (b) is correct.   smiley

 

And your paragraph proof for  (c)  is also correct.

 

Area of Rectangle 1   =   xy

 

Area of Rectangle 2   =   (kx)(ky)   =   k*x*k*y   =   k*k*x*y   =   k2(xy)   =   k2( Area of Rectangle 1 )

hectictar  Feb 10, 2018
 #2
avatar+92674 
+2

Thanks, hectictar.....here's my input.....

 

C  looks good except for the last part.....it should be this :

 

" For Rectangle 2 the area formula would be (kx)(ky)=k^2*xy. Which would make Rectangle  k^2 times the area of Rectangle 1. "

 

[We don't need the "2"  ]

 

For B....consider this

 

The  perimeter  of the original rectangle   = ( 2x  + 2y) .  And the sides of the "new rectangle" are kx  and ky. So its perimeter is 2 (kx)  + 2(ky)  =  k (2x + 2y)  =   "k" times the perimeter of  the first.

 

Hope that helps   !!!!

 

 

cool cool cool

CPhill  Feb 10, 2018
edited by CPhill  Feb 10, 2018
 #3
avatar+7339 
+2

"Which would make Rectangle 2 k^2 times the area of Rectangle 1"

 

Does this mean...

 

it would make Rectangle   2k2   times the area of Rectangle 1

 

or

 

it would make  Rectangle 2   k2 times the area of Rectangle 1

 

?

 

That is the question! smiley

hectictar  Feb 10, 2018

5 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.