SOLUTION: a picture frame is 20cm by 12cm. there are 84cm (to the second power) showing. find the width of the frame

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Question 82612This question is from textbook Algebra 1
: a picture frame is 20cm by 12cm. there are 84cm (to the second power) showing. find the width of the frame This question is from textbook Algebra 1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
20X12 cm are the outside dimensions of the frame
84 cm2 is the area of the frame
Call the width w
divide the top bottom and 2 sides into strips
20w+%2B+20w+%2B+%2812-2w%29%2Aw+%2B+%2812-2w%29%2Aw+=+84
40w+%2B+2w%2A%2812-2w%29+=+84
40w+%2B+24w+-+4w%5E2+=+84
rearranging
4w%5E2+-+64w+%2B+84+=+0
divide both sides by 4
w%5E2+-+16w+%2B+21+=+0
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a+=+1, b+=+-16, c+=+21
w+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A21+%29%29%2F%282%2A1%29+
w+=+%2816+%2B-+sqrt%28256-84+%29%29%2F2+
w+=+%2816+%2B-+sqrt%28172%29%29%2F2+
w+=+%2816+%2B+13.11%29+%2F+2 and
w+=+%2816+-+13.11%29+%2F+2
The 1st answer doesn't make sense, so pick the 2nd
w+=+2.89%2F2
w+=+1.44cm answer