Please help answer my word problem.

Question

 The length of a rectangle is 2 cm less than five times the width. the area of the rectangle is 16 cm^2. find the length and width of the rectangle.

Answer 1

Hi Caity - to answer this question I would suggest setting up a system of equations. You will need 2 equations

 

1) Area (Length * Width) = 16 cm²   

2) Length = 5*Width - 2

 

Since you need to multiply L * W, you can substitute "5*Width - 2" for L, and rewrite it as

 

Area = L * W = (5*W - 2) * W = 16

 

Next, distribute the W:

 

(5*W - 2) * W = 5 * W² - 2 * W = 16

 

Next, subtract 16 from each side to set the equation equal to 0

 

5 * W² - 2 * W - 16 = 0 

 

Finally, solve using either factoring or the quadratic formula. This factors into 

 

(W-2)*(5W + 8) = 0

 

Therefore, 

 

W-2 = 0

or

5W + 8 = 0

 

Let's look at each one separately 

 

W-2 = 0 ... so W = 2

5W + 8 = 0 ... so W = -8/5

 

The width is either 2 or -8/5, but since Width cannot be number, it must be 2

 

Finally, 

 

If the Width is 2, plug 2 back into the equation for Length...Length = (5*W - 2) = 5 * 2 - 2 = 8

 

In conclusion,

 

Width = 2 cm

Length = 8 cm

 

The area is 16 cm² and the Length is 5 times the Width - 2

 

 

Answer 2

w represents the width

5w - 2 represents the length

 

16 = w(5w - 2)

 

Can you solve for w and answer?