SOLUTION: If the perimeter of a rectangle is p and its diagnoal is d, the difference between the length and width of the rectangle is ______? I have worked several formulas, 2L Plus 2W =

Question 892582: If the perimeter of a rectangle is p and its diagnoal is d, the difference between the length and width of the rectangle is ______?
I have worked several formulas, 2L Plus 2W = p, solved for L, and tryig to solve for W, I have worked it several ways. I have also used the Pathagoreum theorm, L squared plus w squared = d squared. I have not been able to solve it, begining to wonder if it is a trick problem from instructor. Can you help.
Answer by josgarithmetic(39799) (Show Source): You can put this solution on YOUR website!
This can only be done using variables because no values are given.

and ;
You want to find .
You assume that the constants are d and p.

;
substitute into the diagonal equation.

Use the general solution of quadratic equation.

AMP Parsing Error of [w=(4p+- 4sqrt(p^2-2(p^2-d^2))/16]: Invalid expression. Closing bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 187. .

-----this is just for w.

What about the other dimension, L?
... w=(p-2L)/2;
when substituted into the diagonal equation.

General Solution,

AMP Parsing Error of [L=(4p+- 4sqrt(p^2-2(p^2-d^2))/16]: Invalid expression. Closing bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 187. .

-----formula for L.

YOU can finish this.
Pay attention to both forms for w and L, since each has a PLUS form and a MINUS form. Remember, you are looking for THE DIFFERENCE or absolute value of w and L.

Please excuse the lack of rendering in three of the steps. Tracing the parentheses will be difficult. The majority of readable steps should be plenty helpful.
RELATED QUESTIONS
The difference between the length and the width of a rectangle is 7 centimeters. Find the (answered by 067isa)

the difference between the length and width of a rectangle is 7 centimeters. what is the... (answered by oberobic)

the difference between the length and width of a rectangle is 7 centimeters. find the... (answered by stanbon)

the difference between the length and width of a rectangle is 7 centimeters. FInd the... (answered by TimothyLamb)

A rectangle has a perimeter of 140cm. The length of the rectangle is three times the... (answered by dkppathak,josgarithmetic)

If the perimeter of a rectangle is 26ft and the width is 9ft, find its length. [Hint:The... (answered by kiljoy)

the area of a rectangle is 56 and its perimeter is 30. find the difference of its length... (answered by josgarithmetic,hamsanash1981@gmail.com)

The difference etween the length and width of a rectangle is 7 centimeters. Find the... (answered by Greenfinch)

If the perimeter of a rectangle is 42" and its width is 6" find its length? (answered by rfer)