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 3cm 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