SOLUTION: what is the step by step solution to "A poster is 25 cm taller than it is wide. It is mounted on a piece of particle board so that there is a 5 cm border on all sides. If the area

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Question 210414: what is the step by step solution to "A poster is 25 cm taller than it is wide. 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 1350 cm squared, what are the dimensions of the poster?"
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the poster =
w cm
The height then =
w+%2B+25 cm
given:
The area of the border is 1350 cm2
The width of the particle board will =
w+%2B+5+%2B+5+=+w+%2B+10 cm
The height of the particle board will =
w+%2B+25+%2B+5+%2B+5+=+w+%2B+35 cm
The area of the particle board =
%28w+%2B+10%29%28w+%2B+35%29 cm2
The area of the poster =
%28w+%2B+10%29%28w+%2B+35%29+-+1350 cm2
The area of the poster is also
w%2A%28w+%2B+25%29
w%2A%28w+%2B+25%29+=+%28w+%2B+10%29%28w+%2B+35%29+-+1350 cm2
w%5E2+%2B+25w+=+w%5E2+%2B+45w+%2B+350+-+1350
25w+=+45w+-+1000
20w+=+1000
w+=+50 cm
w+%2B+25+=+75 cm
The dimensions of the poster are 50 cm x 75 cm
check:
w%2A%28w+%2B+25%29+=+%28w+%2B+10%29%28w+%2B+35%29+-+1350 cm2
50%2A%2850+%2B+25%29+=+%2850+%2B+10%29%2850+%2B+35%29+-+1350
50%2A75+=+60%2A85+-+1350
3750+=+5100+-+1350
3750+=+3750
OK