The length of a rectangle is 5 centimeters less than twice its width. Its area is 42 square centimeters. Find the dimension of the rectangle.

Question

The width is???

Answer 1

If the width is W

then the length is 2W-5

 

W(2W-5)=42

2W²-5W = 42

2W²-5W-42 = 0

 

Factor by grouping or do the quadratic equation.

Multiply the coefficient of the squared term.. 2..

by the constant ..-42..   2(-42)=-84

Factors of -84 that add to the coefficient..-5.. of

the W term are  7(-12)

Replace the -5W with  -12W + 7W

 

2W²-12W+7W-42 = 0

2W(W-6) + 7(W-6)=0

(2W+7)(W-6)=0

 

Either:   2W+7 = 0   or   W-6 = 0

             2W = -7           W = 6 cm

             W = -7/2 cm

 

Since W will not be a negative, our width is 6cm

 

The length is 2W-5 = 2(6)-5=12-5 = 7 cm

 

Hope this helps.  Let me know it there are any questions.

Good luck in your class.

Answer 2

Let the length be l and width be y

 

L = 2w - 5

 

L * w = 42

 

(2w -5)(w) = 42

 

2w^2 -5w - 42 = 0

 

Now solve the quadratic to find the width