The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 23 square centimeters, what is the length of the diagonal?

Question

I need the answer to be accurate to two decimal places. It would be great if you could show how to solve it with a quadratic equation. 

Answer 1

A = 23 = L times W

W =  2L - 6

 

23 = L * (2L - 6)

 

0 = 2L **2 - 6L - 23

 

Here is a related answer from last year:

 

The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 102 square centimeters, what is the length of the diagonal?
Note: Your answer must be a number accurate to two decimal places.
Sep 11 | Blade from Eau Claire, WI | 1 Answer | 0 Votes

Stephen K.
Orlando, FL

Write your width W as W = 2L-6. We know that the area of a rectangle is L x W = Area, so substitute your expression for the width in the formula for area to solve for L. Once you have L you should be able to immediately determine the value of W.

Since the sides of a rectangle are at 90° to one another they, along with the diagonal for a right triangle. You can then use the Pythagorean Equation, a² + b² = c², to solve for the length of the diagonal.


Sep 11 | Stephen K.