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The perimeter of a particular rectangle is eight times its width. If the area of the rectangle is 24 in^2, what is the width of the rectangle, in inches?

 Sep 6, 2021
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The perimeter of a particular rectangle is eight times its width. If the area of the rectangle is 24 in^2, what is the width of the rectangle, in inches?    

 

Call the perimeter P, the length L, and the width W.  

 

P = 8W                              given  

P = 2L + 2W                      perimeter is L+W+L+W  

 

8W = 2L + 2W  

6W = 2L  

3W = L  

 

A = L • W  

A = 3W • W  

A = 3W2  

 

24 = 3W2  

8 = W2  

 

W = sqrt(8)  =  2•sqrt(2)  

 

The problem doesn't ask for the length, but by the way L = 6•sqrt(2)  

.

 Sep 7, 2021

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