SOLUTION: A photograph is enlarged to 20cm by 30cm and framed. The frame is to include a border around the photograph equal in area to the photograph. Find the width of the border.

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Question 1145528: A photograph is enlarged to 20cm by 30cm and framed. The frame is to include a border around the photograph equal in area to the photograph. Find the width of the border.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A photograph is enlarged to 20cm by 30cm and framed.
The frame is to include a border around the photograph equal in area to the photograph.
Find the width of the border.
:
Find the area of the photo: 20 * 30 = 600 sq/cm, border is also 600 so the
overall area = 1200 sq/cm
let x = the width of the border therefore:
overall dimensions is (2x+20) by (2x+30)
Area equation
(2x+20)*(2x+30) = 1200
FOIL
4x^2 + 60x + 40x + 600 = 1200
4x^2 + 100x + 600 - 1200 = 0
4x^2 + 100x - 600 = 0
simplify, divide by 4
x^2 + 25x - 150 = 0
You can use the quadratic formula, a=1; b=25; c=-150; but this will factor to:
(x+25)(x-5) = 0
Positive solution
x = 5 cm is the width of the border
:
:
Check this out
(2(5)+20) * (2(5) + 30) =
30 * 40 = 1200