SOLUTION: a framed picture has length 35 cm and width 25 cm. the picture itself has area 375 sq cm. how far is it from the edge of the picture to the edge of frame if the distance is uniform

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Question 189213: a framed picture has length 35 cm and width 25 cm. the picture itself has area 375 sq cm. how far is it from the edge of the picture to the edge of frame if the distance is uniform around the picture?
Found 2 solutions by jonvaliente, checkley75:
Answer by jonvaliente(64) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = distance of the edge of the picture to the edge of the frame
35-2x = length of the picture
25-2x = width of the picture
%2835-2x%29%2A%2825-2x%29=375
875-120x%2B4x%5E2=375
Subtracting 375 from both sides, and re-arranging the terms, we get:
4x%5E2-120x%2B500=0
Factoring, we get:
%284x-20%29%2A%28x-25%29=0
So,
4x-20=0 and/or x-25=0
4x=20 x=25
x=5
We take x=5, because if x=25, then it would make the length of the picture
(35-2x)=35-2*25=35-50=-15 and length cannot be negative.
So the edge of the picture is 5cm away from the edge of the frame.

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
25*35=875 is the total area.
875-375=500 is the area of the border.
(25-2x)(35-2x)=500
875-120x+4x^2=500
4x^2-120x+875-500
4x^2-120x+375
Using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ we get:
x=(120+-sqrt[-120^2-4*4*375])/2*4
x=(120+-sqrt[14,400-6,000])/8
x=(120+-sqrt[8,400}/8
x=(120+-91.65)/8
x=(120-91.65)/8
x=28.35/8
x=3.54 ans for the width of the border.
Proof:
(25-2*3.54)(35-2*3.54)=500
(25-7.08)(35-7.08)=500
(17.92*27.92)=500
500=500