SOLUTION: A Picture frame measures 12cm by 8cm and is surrounded by a frame whose area is 52cm squared. Find the width of the frame in cm correct to 3 significant figures.

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Question 1004910: A Picture frame measures 12cm by 8cm and is surrounded by a frame whose area is 52cm squared. Find the width of the frame in cm correct to 3 significant figures.
Answer by fractalier(6550) About Me  (Show Source):
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Call the extra part of the length and width, x.
Thus the framed dimensions are 12+x and 8+x.
Originally the frame's area is 12x8 = 96 cm^2
With the frame added on, the new total area is 96 + 52 = 148 cm^2.
So we have
(12+x)(8+x)=148
x^2 + 20x + 96 = 148
x^2 + 20x - 52 = 0
This won't factor, so we apply the quadratic formula...
x = (-20 +- sqrt(20^2 + 208)) / 2
x = (-20 +- sqrt(608)) / 2
x = -10 +- sqrt(152)
We must use the positive root and get
x = -10 + 12.33 = 2.33
So the dimensions of the framed picture are approximately 14.33 cm by 10.33 cm.