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?

Oct 21, 2017

W = 50 cm & L = 75 cm

Explanation:

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
$\Rightarrow \left(35 + x\right) \left(x + 10\right) - 25 x - {x}^{2} = 1350$

$\Rightarrow 35 x + 350 + {x}^{2} + 10 x - 25 x - {x}^{2} = 1350$

$\Rightarrow 20 x = 1000$

$\Rightarrow x = 50$

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