The width of a rectangle is 6 less than twice its length. if the area of the rectangle is 110 cm^2, what is the length of the diagonal?

 the answer is: 9.16485485837795, -6.16485485837795. but if you need the work here it is
Step 2. Let 2L-6 be the width since the width of a rectangle is 6 less than twice its length. 

Step 3. Area A=113=L*(2L-6) 

Step 4. Solving for L yields the following steps 

 

Subtract 113 from both sides of the equation to get a quadratic equation 

 

 

To solve for L, we can use the quadratic formula given as 

 

where a=2, b=-6 and c=-113 

Solved by pluggable solver: SOLVE quadratic equation with variableQuadratic equation  (in our case ) has the following solutons:

For these solutions to exist, the discriminant  should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=940 is greater than zero. That means that there are two solutions: .

Tje answer will be something around 6.1