# A window manufacturer makes a range of windows for which the height is 50 cm greater than the width. Find the width and height of a window with an area of 2.34 square meters.

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### 1 Answer

The window manufacturer makes a range of windows for which the height is 50 cm greater than the width.

Let the width of the window be x cm., the height of the window is x + 50 cm. The area of the window is x(x+50) = 2.34*1000 = 23400

=> x^2 + 50x - 23400 = 0

=> x^2 + 130x - 180x - 23400 = 0

=> x(x + 130) - 180(x + 130) = 0

=> (x - 180)(x + 130) = 0

The positive root of the equation is 180.

The height of the window is 230 cm and the width is 180 cm.It has to be either one of these...

width:1.1m, height: 1.6m

width:1.2m, height = 1.7m

width:1.3m, height = 1.8m

width = 1.4m, height = 1.9m

The previous solution is incorrect.

Let x=width and x+50=height.

Therefore, `x*(x+50)=` Area of the Window.

But, the units are different. The dimensions of the window are given in centimeters, but the area is given in meters squared. Therefore, we must convert the dimensions of the window into meter units. (100cm=1m)

`x/100 * (x+50)/100 = 2.34` , where all values are now in meters.

`=> x*(x+50)=2.34*100*100`

`=> x^2+50x=23400`

`=> x^2+50x-23400=0`

`=> (x+180)*(x-130)=0`

Dimensions cannot have a negative value; thus, the only value of x that would satisfy this equation is `130` .

**x=width=130cm=1.3m**

**x+50=height=180cm=1.8m**