a picture frame is shaped like a rectangle. the length of the frame is 3 centimeters more than the width. the area is 108 square meters. find the length of the picture frame.

Question

Apples17 Apples17

20-11-2014
Mathematics

Answered

a picture frame is shaped like a rectangle. the length of the frame is 3 centimeters more than the width. the area is 108 square meters. find the length of the picture frame.

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kriquier kriquier · Answer 1 · 2014-11-20T21:27:08-05:00

Area=length × width
Area=108
Let Width=X
Let Length=X+3
So now you have 108=X(X+3)
Multiply x by the number/varialbe in the parenthesis and you will get 108=x²+3x
Now you would move 108 to the others side and now you have x²+3x-108=0
Now you want to factor it out. What multiplies to get 108 and adds to be 3? This would be -9 and 12
So now you have it factored out (x-9)(x+12)=0
Now you let both of those factors equal 0. And you will have x-9=0 and x+12=0. Isolate the variable and you have x=9 and x=-12. They both make the equation correct, but in this situation, only 9 works because you can not have negative lengths.