SOLUTION: Can anyone seem to help me with this problem? I have come to a complete blank on it. Question 64 Address book The perimeter of the cover of an address book is 14 inches, a

Question 151681: Can anyone seem to help me with this problem? I have come to a complete blank on it.

Question 64
Address book
The perimeter of the cover of an address book is 14 inches, and the diagonal measures 5 inches. What are the length and width of the cover?
x^2 + x^2 = 5^2
x^4 = 25
x^4 - 25 = 14
I do not know what to do next. I followed the Pythagorean steps, but cannot figure out what has gone wrong.
Thanks.
Amanda

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=width and y=length

Remember, the perimeter of any rectangle is:

Plug in (the given perimeter)

Subtract from both sides.

Rearrange the terms

Divide both sides by 2 to isolate y

Through the use of pythagoreans theorem, we get:

Square 5 to get 25

Plug in

FOIL

Subtract 25 from both sides.

Combine like terms. Note:

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the widths are or

Go back to the second equation

Plug in

Add

So if the width is 4 inches, the length is 3 inches

------------------------------------

Go back to the second equation

Plug in

Add

So if the width is 3 inches, the length is 4 inches

Note: the length is usually the longer of the two. So your book probably has the width of 3 inches and a length of 4 inches

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