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The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimension of the rectangle.

 

a) L = 5cm; W = 18cm

 

b) L = 13cm; W = 8cm

 

c) L = 13cm; W = 5cm

 

d) L = 18cm; W = 5cm

 

L = Length 

W = Width

 Nov 5, 2020
 #1
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The correct answer is     d) L = 18cm; W = 5cm

 Nov 5, 2020
 #2
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The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimension of the rectangle.     

 

Call the length L and call the width W  

 

Here's the relationship between their sizes:                                        L = 3W + 3 

 

The perimeter is two times the length plus two times the width  

 

So ...                                                                                              2(L)          + 2(W)  =  46  

 

Remember L = 3W + 3 so substitute it in the place of L                 2(3W + 3) + 2(W)  =  46  

 

Multiply it out                                                                                  6W + 6      + 2W    =  46   

 

Combine like terms                                                                         8W   +   6              =  46   

 

Subtract 6 from each side                                                              8W                         =  40  

 

Divide both sides by 8                                                                                            W  =  5  

 

Plug this back into L = 3W +3                                                          L  =  3(5) + 3 = 15 + 3   

 

                                                                                                                               L  =  18  

.

 Nov 5, 2020
 #3
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Thank you! This was really helpful.

SmartMathMan  Nov 5, 2020

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