SOLUTION: A picture frame measures 12 cm by 20 cm, and 84 cm^2 of picture shows. Find the width of the frame.

Question 26530: A picture frame measures 12 cm by 20 cm, and 84 cm^2 of picture shows. Find the width of the frame.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Over-all area is 12(20)=240 sq.cm.
240 sq.cm.-84cm^2=156 cm^2 (This is the area in the frame.
Let the width of the frame all around the picture be "x"
The frame is made of four rectangles.
Dimensions of two of the rectangles are (12)by (x)
Area involved = 2x(12)=24x
Dimensions of the other two rectangles are (x)by(20+2x)
Area involved =2x(20+2x)=40x+4x^2
EQUATION:
Total frame area =156
24x+40x+4x^2=156
4x^2+64x-156=0
x^2+16x-39=0
Using the quadratic formula get:
x=[-16+-sqrt(16^2-4(-39)]/2
x=[-16+2sqrt103]/2
x=[-8+sqrt103{=2.15 cm.
Cheers,
Stan H.

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