The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 54 square​ centimeters?

2 Answers
Feb 27, 2018

Width#=9cm#
Length#=6cm#

Explanation:

Let #x# be width, then length is #x-3#
Let area be #E#. Then we have:
#E=x*(x-3)#
#54=x^2-3x#
#x^2-3x-54=0#

We then do the Discriminant of the equation:

#D= 9+216#
#D=225#

#X_1 = (3 + 15)/2 = 9#
#X_2 = (3-15)/2 = -6# Which is declined, since we can't have negative width and length.

So #x=9#
So width #= x = 9cm# and length#=x-3=9-3=6cm#

Feb 27, 2018

Length is #6cm# and the width is #9cm#

Explanation:

In this question, the length is less than the width. It does not matter at all - they are just names for the sides. Usually the length is longer, but let's go with the question.

Let the width be #x#
The length will be #x-3" "# ( it is #3#cm less)

The area is found from #l xx w#

#A = x(x-3) =54#

#x^2-3x -54 =0" "larr# make a quadratic equation equal to #0#

Factorise: Find factors of #54# which differ by #3#

#(x" "9)(x" "6)=0#

There must be more negatives: #" "# because of #-3x#

#(x-9)(x+6)=0#

Solve for #x#

#x-9=0" "rarr x =9#

#x+3=0" "rarr x =-3" "# reject as the length of a side.

the width is #9cm# and the length is #9-3 =6cm#