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Geometry problem please help: rectangular picture

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Source: — Problem Solving |
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by netigen » Thu May 29, 2008 9:06 pm
let l = length of the picture and
let w = width of the picture

l/w = 18/15 ----> same proportions
l x w = 18 x 15 - l x w ---> same area
lw = 15 x 9 = 135

w = 135 /l

substitute,

l^2 = 18/15 x 135 = 18 x 9
l = 9 sqrt(2)
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by getneonow » Thu May 29, 2008 10:17 pm
netigen wrote:let l = length of the picture and
let w = width of the picture

l/w = 18/15 ----> same proportions
l x w = 18 x 15 - l x w ---> same area
lw = 15 x 9 = 135

w = 135 /l

substitute,

l^2 = 18/15 x 135 = 18 x 9
l = 9 sqrt(2)
Can you elaborate on the part in bold?

Area of frame = 18 * 15 only ..

and l* w is the area of the rectangular picture.

The question wording i felt is not clear.

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by netigen » Thu May 29, 2008 10:23 pm
from the given diagram

18x15 = total area = area of the frame + area of the picture
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by ksh » Fri May 30, 2008 3:00 am
Hi wawatan,

Area of frame+picture=18*15
suppose x and y be the length and breadth of the picture in meteres respectively.
Given area of picture=area of frame
so, 18*15-xy=xy
2xy=18*15=> xy=15*9-----eqn 1
also given x/y=18/15
so, y=15x/18
from eqn1 x*15x/18=15*9
x^2=18*15*9/15=18*9
therefore, x=9sqrt2. is the ans
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