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

2 Answers
Mar 25, 2018

#"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"#

Mar 25, 2018

#"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#