Question

A rectangle has a length of 25 meters less than 6 times its width. If the area of therectangle is 261 square meters, find the length of the rectangle.

Answer 1

Let the length be x and width be y.

As per the condition:

$x=6y-25$

As per the second condition:

$xy=261$

Combine the two conditions to get:

$\begin{gathered} y(6y-25)=261 \\ 6y^2-25y-261=0 \\ y=9,\frac{-29}{6} \end{gathered}$

Since length is never negative, y=9.

hence the length is given by:

$\begin{gathered} x=6y-25 \\ x=6(9)-25 \\ x=29 \end{gathered}$

Hence the length of the rectangle is 29 meters.