The length of a rectangle is 23 centimeters less than six times its width. Its area is 35 square centimeters. Find the dimensions of the rectangle.

Question

Thank you for your help

Answer 1

Let L = length

Let W = width

Let A = area

 

The area of a rectangle is length * width, so we know that A = L * W

 

From the description, we know the following:

 

L = 6W - 23 

A = 35

 

Therefore, if we plug L and A into the first equation, we get this:

 

35 = (6W-23)*W

35 = 6W²-23W

6W²-23W - 35 = 0

 

We're going to factor this equation to solve for W.

 

We know that -35 only has a few factors (-35 and 1, 35 and -1, -7 and 5, or 7 and -5).

So we have the following:

 

(6W +- a)(W +-b) = 0

 

We know that 6W*b + W*a = -23W, so 6W*b = -30 and W*a = 7.

 

Therefore:

 

(6W + 7)(W - 5) = 0

 

Negative width makes no sense, so the first factor can be completely ignored.

Since W-5=0, W = 5

 

If W = 5, and W * L = 35, then L = 7