So that there is a 5 cm border on all sides. if the area of the border alone
is 1350 cm^2, what are the dimensions of the poster?
Let x = width of the poster
Then (x+25) = length of the poster
Area of the poster = x(x+25 = (x^2 + 25x)
(x + 2(5)) = width of the cardboard the poster is mounted on
(x+10) = width simplified
(x + 25 + 2(5)) = length of cardboard
(x + 35) = length simplified
Area of cardboard = (x+10)*(x+35) = (x^2 + 45x + 350)
(x^2 + 45x + 350) - (x^2 + 25x) = 1350
x^2 + 45x + 350 - x^2 - 25x = 1350
x^2 - x^2 + 45x - 25x + 350 = 1350
20x + 350 = 1350
20x = 1350 - 350
20x = 1000
x = 1000/20
x = 50 cm is the width of the poster
50 + 25 = 75 cm is the length of the poster
Check:
(85*60) - (75*50)
5100 - 3750 = 1350 sq/cm the given area of the border
Ok? gets?
