This one is 'less' than twice the width

Question

The length of a rectangle is
3
meters less than twice the width. If the area of the rectangle is
527
square? meters, find the dimensions.

Answer 1

We know that the formula for area of a rectangle is A=lw. The length given in the problem is l=2w-3. This makes the equation A=(2w-3)(w). We know the area, so all we have to do is solve.

527=(2w-3)(w)

527=2w²-3w

2w²-3w-527=0

We will use the quadratic formula to determine what w equals

-(-3)±√((-3)²-(4)(2)(-527))

----------------------------------

                  2(2)

3±√((9)-(-4216))

-----------------------

               4

3±65

------

   4

68/4=17=w

measurements cannot be negative, so we only add.

We now know that the length equals 17, so when we go back to our original equation, we can solve for length and get the dimensions of the rectangle

527=17l

 

l=31

The dimensions are l=31 meters, w=17 meters.