A poster is 25 cm taller than it is wide. It is mounted on a piece of card board 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?

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Answer 1 · 2017-10-21T03:16:09

W = 50 cm & L = 75 cm

Let the width be x cm. so, length will be 25+x cm. Hence area of the poster = (25+x)x sq cm.

It is mounted on card board with 5cm bordered.

So,length of The board = 25+x+10 cm & width x+10 cm. Area of the board = (25+x+10)(x+10) sq cm.

The area of the border = (25+x+10)(x+10) - x(25+x) sq cm

Now,as per question,
(25+x+10)(x+10)-x(25+x)=1350
#rArr (35+x)(x+10)-25x-x^2=1350#

#rArr 35x+350+x^2+10x-25x-x^2=1350#

#rArr 20x=1000#

#rArr x=50#

Hence, width = 50 cm & length = 50+25=75cm