The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 238 square​ centimeters?

Question

The length and width of the rectangle

Answer 1

Hello Jimin,

 

Let W = the width of the rectangle, and L = the length.

 

Then L = W - 3.

 

From that, since area of a rectangle is length X width,

 

⇒ A = L * W

⇒ A = (W - 3) * W

⇒ A = W² - 3W.

 

We are told that the area is 238,

⇒ W² - 3W = 238

⇒ W² - 3W - 238 = 0

 

Looking for two numbers which multiply to 238, but add or subtract to 3, we can factor as

(W - 17) * (W + 14) = 0

⇒ W = 17 or -14.

 

But -14 wouldn't make sense for the width, so

W = 17

⇒ L = 14

 

So the dimensions are 17 by 14.

 

Hope the above helps.  Should you have any questions on it, please feel free to message me directly.

 

Kind regards,

Michael E.

Answer 2

w(w-3) = 238

 

that is a quadratic equation and you should solve it for w.