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The length of a rectangle is 12 centimeters less than its width. What are the dimensions of the rectangle if it’s area is 85 square centimeters?

 Feb 13, 2020
 #1
avatar+109740 
+2

Let the width   = W

Let the length, L = W - 12

 

Area =  W * L

 

So.....

 

85 = W ( W - 12)    simplify

 

85  = W^2 - 12W      rearrange as

 

W^2 -12W  - 85    =  0       factor

 

(W+ 5) (W -17)  =   0

 

Setting both factors to 0  and solving for  W produces

 

W  = - 5    (reject)

 

W =  17  (accept)

 

And L  =  W - 12   = 17 - 12  =   5

 

 

cool cool cool

 Feb 13, 2020
 #2
avatar+302 
+1

Let's make "x" the width.

Length = x-12.

 

Area of rectangle: Width * Length.

 

This means: x(x-12) = 85.

 

Simplifying that is: x^2 - 12x = 85.

 

Rearranging it: x^2 - 12x - 85 = 0.

 

Factor it: (x+5)(x+17)-85 = 0

 

We can set both factors to 0 and solve for x:

 

x = -5 which doesn't work

 

x = 17 which works.

 

And for the Length: x - 12 = 17 -12 = 5.

 

I used the same method as CPhill though...

 Feb 13, 2020

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