Question

The area of a rectangle is $640m^2$. Taking its length as x m; find in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.

• A. $Width=\frac{640}{x}m;32mand20m$
• B. $Width=\frac{320}{x}m;42mand10m$
• C. $Width=\frac{640}{x}m;22mand30m$
• D. $Width=\frac{640}{x}m;44mand8m$

Answer 1

The correct option is A $Width=\frac{640}{x}m;32mand20m$

Given,
Area of rectangle=$640m^2$ and
Perimeter of rectangle=$104m$
Let, length of the rectangle=$xcm$ and
Width of the rectangle=$ycm$
Therefore,
$xy=640$
$=>y=\frac{640}{x}$
Therefore,
Width=$\frac{640}{x}$
Now,
$2(x+y)=104$
$=>x+y=52$
$=>x+\frac{640}{x}=52$
$=>x^2-52x+640=0$
$=>x-32x-20x+640=0$
$=>x-(x-32)-20(x-32)=0$
$=>(x-32)(x-20)=0$
Therefore,
$x=32$ or, $x=20$
Therefore,
$y=20m$ or, $y=32m$