Question 80698
A rectangle is initially 6cm wide and 12cm long. If a strip of uniform width is added to the outside of each of the four sides, the resulting area is 160 square cm. Determine the width of the strip?
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Draw the picture of the rectangle.
Draw the stip bordering the rectangle but outside it.
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Let the width of the stip be "x" cm.
Area of the resulting rectangle including the border is:
(6+2x)(12+2x)= 160 sq cm.
4(3+x)(6+x)=160
[18+9x+x^2)= 40
x^2+9x-22=0
(x+11)(x-2)=0
Positive answer: x=2 cm
This is the width of the border.
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Checking: (6+2*2)(12+2*2)= 10*16=160
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Cheers,
Stan H.