SOLUTION: A picture is 10cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5cm border on all sides. If the area of the border is alone 580cm squared, what a

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Question 130098: A picture is 10cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5cm border on all sides. If the area of the border is alone 580cm squared, what are the the dimensions of the picture?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= the width
The height will be x+%2B+10
The area of the picture is then x%2A%28x+%2B+10%29
Including the border, the width is x+%2B+5+%2B+5
Including the border, the height is x+%2B+10+%2B+5+%2B+5
%28x+%2B+5+%2B+5%29%28x+%2B+10+%2B+5+%2B+5%29+=+580+%2B+x%2A%28x+%2B+10%29
%28x+%2B+10%29%28x+%2B+20%29+=+580+%2B+x%5E2+%2B+10x
x%5E2+%2B+30x+%2B+200+=+580+%2B+x%5E2+%2B+10x
20x+=+580+-+200
x+=+19
x+%2B+10+=+29
The dimensions of the picture are 19 x 29
check answer:
Adding up the pieces of the border,
580+=+2%2A5%2A19+%2B+2%2A5%2A29+%2B+4%2A5%5E2
580+=+190+%2B+290+%2B+100
580+=+580
OK
The area of the border + picture is
19+%2B+5+%2B+5%29%2829+%2B+5+%2B+5%29
29%2A39+=+1131
1131+-+580+=+551
19%2A29+=+551
OK