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 centimeters. Find the length of the picture frame.
Answer (2)
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.
The length of the picture frame is 12 centimeters, calculated by first defining the width as a variable, setting up the area equation, and solving a quadratic equation to find valid dimensions.
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