SOLUTION: A poster is 25 cm taller than its width. It is mounted on a piece of particle board so that there is a 5 cm border on all sides. If the area of the border alone is 1250 sq cm, what
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Question 153364: A poster is 25 cm taller than its width. It is mounted on a piece of particle board so that there is a 5 cm border on all sides. If the area of the border alone is 1250 sq cm, what are the dimensions of the poster?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A poster is 25 cm taller than its width. It is mounted on a piece of particle board so that there is a 5 cm border on all sides. If the area of the border alone is 1250 sq cm, what are the dimensions of the poster?
:
Let x = width of the poster
:
It says the height is 25 cm more than the width, therefore
(x+25) = height of the poster
Then
x(x+25) = x^2 + 25x = the area of the poster
:
Find overall area of the particle board; (add 10 cm to the poster dimensions):
(x+35)*(x+10) = x^2 + 45x + 350 = overall area
:
The equation:
overall area - poster area = border area (given as 1250 sq/cm)
(x^2 + 45x + 350) - (x^2 + 25x) = 1250
:
Remove brackets, group like terms:
x^2 - x^2 + 45x - 25x + 350 = 1250
:
20x + 350 = 1250
:
20x = 1250 - 350
:
20x = 900
x =
x = 45 cm is the width of the poster
and
45 + 25 = 70 cm is the height of the poster
:
:
Check solution
(55*80) - (45*70) =
4400 - 3150 = 1250; confirms our solutions
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