Question

The length of a rectangle is four times the width. The area is 1444. How do you find the width and length?

Answer 1

`"width "=19," length "=76`

Explanation:

`"let the width "=w`

`rArr"length "=4wlarrcolor(blue)"four times the width"`

`• " area of rectangle "="length "xx"width"`

`rArr"area "=4wxxw=4w^2`

`"now area "=1444`

`"equating the expression and given value for area"`

`rArr4w^2=1444`

`"divide both sides by 4"`

`(cancel(4) w^2)/cancel(4)=1444/4`

`rArrw^2=361`

`color(blue)"take the square root of both sides"`

`rArrw=+-sqrt361larrcolor(blue)"note plus or minus"`

`rArrw=+-19`

`"but "w>0rArrw=19larrcolor(red)"width"`

`"and "4w=(4xx19)=76larrcolor(red)"length"`

Answer 2

`"width" = 19`, `"length" = 76`.

Explanation:

Another way of thinking about this...

If we double the width and halve the length, then the rectangle will have the same area `1444`, but it will be a square with sides `sqrt(1444) = 38`.

So the original length of the rectangle is `2 * 38 = 76` and width `38 / 2 = 19`