SOLUTION: A picture measures 12cm by 20cm. We wish to add a border of equal width around the frame. The area of the border must equal the area of the picture. Determine the width of the bord

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A picture measures 12cm by 20cm. We wish to add a border of equal width around the frame. The area of the border must equal the area of the picture. Determine the width of the bord      Log On


   

Question 1106181: A picture measures 12cm by 20cm. We wish to add a border of equal width around the frame. The area of the border must equal the area of the picture. Determine the width of the border correct to one decimal place
Answer by ikleyn(52778) About Me  (Show Source):
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The dimensions of the picture are 12 by 20 cm.

If the width of the border is "w" cm,  then the outer dimensions become 12+2w by 20+2w centimeters.

The new area is (12+2w)*(20+2w) cm^2;  the old area is 12*20 cm^2;  the border area is the difference (12+2w)*(20+2w) - 12*20 cm^2. 

The condition requires 

(12+2w)*(20+2w) - 12*20 = 12*20,

which gives you a quadratic equation

12*20 + 40w + 24w + 4w^2 - 12*20 = 12*20,   or

4w^2 + 64w - 240 = 0,   or

w^2 + 16w - 60 = 0.

w%5B1%2C2%5D = %28-16+%2B-+sqrt%2816%5E2+%2B+4%2A60%29%29%2F2 = %28-16+%2B-+sqrt%28496%29%29%2F2 = -8+%2B-+sqrt%28124%29 = -8+%2B-+2%2Asqrt%2831%29.


Only positive root suits w = -8+%2B+2%2Asqrt%2831%29 = 3.1 cm.


Answer.  w = 3.1 cm approximately with one decimal correct after decimal dot.

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To see many other solved similar problems, look into the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".