SOLUTION: A rectangular picture is 3 cm longer than it is wide. The picture is surrounded by a frame that is 2 cm wide. The area of the picture and the frame together is 1000cm^ greater than
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Question 706441: A rectangular picture is 3 cm longer than it is wide. The picture is surrounded by a frame that is 2 cm wide. The area of the picture and the frame together is 1000cm^ greater than the area of the picture. I need to find the width of the picture.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular picture is 3 cm longer than it is wide.
The picture is surrounded by a frame that is 2 cm wide.
The area of the picture and the frame together is 1000cm^ greater than the area of the picture.
I need to find the width of the picture.
:
let w = the width of the picture
then
(w+3) = the length of the picture
and
w(w+3) = w^2 + 3w; the area of the picture
:
The overall area; add 4 cm to the length and the width of picture
W = (w+4)
L = (w+7)
A = (w+4)(w+7) = w^2 + 11w + 28; the overall area of the frame and picture
:
Overall area - picture area = 1000 cu/cm
w^2 + 11w + 28 -(w^2 + 3w) = 1000
combine like terms
w^2 - w^2 + 11w - 3w = 1000 - 28
8w = 972
w = 972/8
w = 121.5 cm is the width of the picture
then
121.5 + 3 = 124.5 cm is the length of the picture
:
:
YOu can check this: (125.5*128.5) - (121.5*124.5) =
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